isometric dilations for infinite sequences of noncommuting operators this paper develops a dilation theory for t n l an infinite sequence of noncommuting operators on a hilbert space when the matrix t1 t2 is a contraction a wold decomposition for an infinite sequence of isometries with orthogonal final spaces and a minimal isometric dilation for tn i are obtained some theorems on the geometric structure of the space of the minimal isometric dilation and some consequences are given this results are used to extend the sz nagy foia lifting theorem to this noncommutative setting this paper is a continuation of 5 and develops a dilation theory for an infinite sequence tn n of noncommuting operators on a hilbert space when en 1 tn tn i i is the identity on s many of the results and techniques in dilation theory for one operator 8 and also for two operators 3 4 are extended to this setting first we extend wold decomposition 8 4 to the case of an infinite sequence vn i of isometries with orthogonal final spaces in 2 we obtain a minimal isometric dilation for tn 1 by extending the schaffer construction in 6 4 using these results we give some theorems on the geometric structure of the space of the minimal isometric dilation finally we give some sufficient conditions on a sequence t7 n to be simultaneously quasi similar to a sequence rn n i of isometries on a hilbert space x with en rnrn n ix in 3 we use the above mentioned theorems to obtain the sz nagy foia5 lifting theorem 7 8 1 4 in our setting in a subsequent paper we will use the results of this paper for studying the characteristic function associated to a sequence tn lo 1 with ez 1 t t i throughout this paper a stands for the set 1 2 k k e n or the set n 1 2 received by the editors september 1 1987 1980 mathematics subject classification 1985 revision primary 47a20 secondary 47a45

isomorphisms of algebras associated with directed graphs given countable directed graphs g and g we show that the associated tensor algebras open image in new window g and open image in new window g are isomorphic as banach algebras if and only if the graphs g are g are isomorphic for tensor algebras associated with graphs having no sinks or no sources the graph forms an invariant for algebraic isomorphisms we also show that given countable directed graphs g g the free semigroupoid algebras open image in new window and open image in new window are isomorphic as dual algebras if and only if the graphs g are g are isomorphic in particular spatially isomorphic free semigroupoid algebras are unitarily isomorphic for free semigroupoid algebras associated with locally finite directed graphs with no sinks the graph forms an invariant for algebraic isomorphisms as well

tensor algebras overc correspondences representations dilations andc envelopes tensor algebras overc correspondences are noncommutative generalizations of the disk algebra they contain as special cases analytic crossed products semi crossed products and popescu s noncommutative disk algebras in this paper a dilation theorem and a commutant lifting theorem for representations of tensor algebras is proved these are used to show that for certainc correspondences thec envelopes in the sense of arveson of the tensor algebras are the cuntz pimsner algebras of the correspondences

invariant subspaces and hyper reflexivity for free semigroup algebras in this paper we obtain a complete description of the invariant subspace structure of an interesting new class of algebras which we call free semigroup algebras this enables us to prove that they are reflexive and moreover to obtain a quantitative measure of the distance to these algebras in terms of the invariant subspaces such algebras are called hyper reflexive this property is very strong but it has been established in only a very few cases moreover the prototypes of this class of algebras are the natural candidate for a non commutative analytic toeplitz algebra on n variables the case we make for this analogy is very compelling in particular in this paper the key to the invariant subspace analysis is a good analogue of the beurling theorem for invariant subspaces of the unilateral shift this leads to a notion of inner outer factorization in these algebras in a sequel to this paper 13 we add to this evidence by showing that there is a natural homomorphism of the automorphism group onto the group of conformal automorphisms of the ball in cn a free semigroup algebra is the weak operator topology closed algebra generated by a set s1 sn of isometries with pairwise orthogonal ranges these conditions are described algebraically by s i sj iji for 1 i j n f

duals of compact lie groups realized in the cuntz algebras and their actions on c algebras abstract as a first step towards a new duality theorem for compact groups we consider a representation category t g of a compact lie group g u d c whose objects are the tensor powers of the defining representation and whose arrows are the intertwiners we associate to t g in a natural way a c algebra og which can be identified with the fixed points of the cuntz algebra od under the natural action of g og carries a canonical endomorphism g and t g can be reconstructed from og g if g su d then og is simple we give conditions for an endomorphism of a unital c algebra a to determine an action of t su d on a such actions correspond to monomorphisms of osu d into a with natural intertwining properties

semi crossed products of c algebras abstract given a c algebra u and endomorphim there is an associated nonselfadjoint operator algebra z x u called the semi crossed product of u with if is an automorphim z x u can be identified with a subalgebra of the c crossed product z x u if u is commutative and is an automorphim satisfying certain conditions z x u is an operator algebra of the type studied by arveson and josephson suppose s is a locally compact hausdorff space s s is a continuous and proper map and is the endomorphim of u c0 s given by necessary and sufficient conditions on the map are given to insure that the semi crossed product z x c0 s is i semiprime ii semisimple ii strongly semisimple

a uniform type inverse spectrum theorem for entrywise nonnegative matrices abstract influenced by earlier results of fiedler m fiedler eigenvalues of nonnegative symmetric matrices linear algebra appl 9 1974 119 142 wuven guo wuven eigenvalues of nonnegative matrices linear algebra appl 266 1997 261 270 established interesting theorems and posed several natural questions in the inverse spectrum problem for entrywise nonnegative matrices we answer some of these of a uniform character obtaining the sharpest possible results

growth type invariants for ℤ d subshifts of finite type and arithmetical classes of real numbers we discuss some numerical invariants of multidimensional shifts of finite type sfts which are associated with the growth rates of the number of admissible finite configurations extending an unpublished example of tsirelson a strange two dimensional symbolic system 1992 we show that growth complexities of the form exp n o 1 are possible for non integer s in terminology of de carvalho port math 54 1 19 40 1997 such subshifts have entropy dimension the class of possible s are identified in terms of arithmetical classes of real numbers of weihrauch and zheng math log q 47 1 51 65 2001

algebraic shift equivalence and primitive matrices motivated by symbolic dynamics we study the problem given a unital subring s of the reals when is a matrix a algebraically shift equivalent over s to a primitive matrix we conjecture that simple necessary conditions on the nonzero spectrum of a are sufficient and establish the conjecture in many cases if s is the integers we give some lower bounds on sizes of realizing primitive matrices for dedekind domains we prove that algebraic shift equivalence implies algebraic strong shift equivalence

order preservation in limit algebras abstract the matrix units of a digraph algebra a induce a relation known as the diagonal order on the projections in a masa in the algebra normalizing partial isometries in a act on these projections by conjugation they are said to be order preserving when they respect the diagonal order order preserving embeddings in turn are those embeddings which carry order preserving normalizers to order preserving normalizers this papers studies operator algebras which are direct limits of finite dimensional algebras with order preserving embeddings we give a complete classification of direct limits of full triangular matrix algebras with order preserving embeddings we also investigate the problem of characterizing algebras with order preserving embeddings

a characterization of operator algebras abstract an operator algebra is a uniformly closed algebra of bounded operators on a hilbert space in this paper we give a characterization of unital operator algebras in terms of their matricial norm structure more precisely if a is an l matricially normed space and also an algebra with a completely contractive multiplication and an identity of norm 1 then there is a completely isometric isomorphism of a onto a unital operator algebra indeed the multiplication on a need not be assumed to be associative for this conclusion to follow examples are given to show that the condition on the identity is necessary it follows from the above that the quotient of an operator algebra by a closed two sided ideal with the natural matricial structure is again an operator algebra up to complete isometric isomorphism

meet irreducible ideals and representations of limit algebras in this paper we give criteria for an ideal j of a taf algebra a to be meet irreducible we show that j is meet irreducible if and only if the c envelope of a j is primitive in that case a j admits a faithful nest representation which extends to a representation of the c envelope for a j we also characterize the meet irreducible ideals as the kernels of bounded nest representations this settles the question of whether the n primitive and meet irreducible ideals coincide

the algebraic structure of non commutative analytic toeplitz algebras the non commutative analytic toeplitz algebra is the wot closed algebra generated by the left regular representation of the free semigroup on n generators we develop a detailed picture of the algebraic structure of this algebra in particular we show that there is a canonical homomorphism of the automorphism group onto the group of conformal automorphisms of the complex n ball the k dimensional representations form a generalized maximal ideal space with a canonical surjection onto the ball of k kn matrices which is a homeomorphism over the open ball analogous to the fibration of the maximal ideal space of h over the unit disk in 6 17 18 20 a good case is made that the appropriate analogue for the analytic toeplitz algebra in n non commuting variables is the wotclosed algebra generated by the left regular representation of the free semigroup on n generators the papers cited obtain a compelling analogue of beurling s theorem and inner outer factorization in this paper we add further evidence the main result is a short exact sequence determined by a canonical homomorphism of the automorphism group onto this algebra onto the group of conformal automorphisms of the unit ball of cn the kernel is the subgroup of quasi inner automorphisms which are trivial modulo the wot closed commutator ideal additional evidence of analytic properties comes from the structure of k dimensional completely contractive representations which have a structure very similar to the fibration of the maximal ideal space of h over the unit disk an important tool in our analysis is a detailed structure theory for wot closed right ideals curiously left ideals remain more obscure the non commutative analytic toeplitz algebra ln is determined by the left regular representation of the free semigroup fn on n generators z1 zn which acts on 2 fn by w v wv for v w in fn in particular the algebra ln is the unital wot closed algebra generated by the isometries li zi for 1 i n this algebra and its norm closed version the noncommutative disk algebra were introduced by popescu 19 in an abstract sense in connection with a non commutative von neumann inequality and 1991 mathematics subject classification 47d25 march 9 1997 october 9 1997 final draft first author partially supported by an nserc grant and a killam research fellowship second author partially supported by an nsf grant

the classification of some generalised bunce deddens algebras abstract we use k theory to prove an isomorphism theorem for a large class of generalised bunce deddens algebras constructed by kribs and solel from a directed graph e and a sequence of positive integers in particular we compute the torsion free component of the k 0 group for a class of generalised bunce deddens algebras to show that supernatural numbers are a complete invariant for this class

semicrossed products of operator algebras and their c envelopes abstract let a be a unital operator algebra and let be an automorphism of a that extends to a automorphism of its c envelope c env a we introduce the isometric semicrossed product a is z and we show that c env a is z c env a z in contrast the c envelope of the familiar contractive semicrossed product a z may not equal c env a z our main tool for calculating c envelopes for semicrossed products is a new concept the relative semicrossed product of an operator algebra by an endomorphism as an application of our theory we show that if t x is the tensor algebra of a c correspondence x a and is a extendible automorphism of t x that fixes the diagonal elementwise then the contractive semicrossed product satisfies c env t x z o x z where o x denotes the cuntz pimsner algebra of x a this extends the main result of davidson and katsoulis 2010 6

compact operators and nest representations of limit algebras in this paper we study the nest representations p a alg n of a strongly maximal taf algebra a whose ranges contain non zero compact operators we introduce a particular class of such representations the essential nest representations and we show that their kernels coincide with the completely meet irreducible ideals from this we deduce that there exist enough contractive nest representations with non zero compact operators in their range to separate the points in a using nest representation theory we also give a coordinate free description of the fundamental groupoid for strongly maximal taf algebras for an arbitrary nest representation p a alg n we show that the presence of non zero compact operators in the range of p implies that n is similar to a completely atomic nest if in addition p a is closed then every compact operator in p a can be approximated by sums of rank one operators p a in the case of n ordered nest representations we show that p a contains finite rank operators iff ker fails to be a prime ideal

a three wave interaction model with self consistent sources the dressing method and solutions abstract in the paper we study the three wave interaction model with self consistent sources by virtue of the dressing method the explicit solutions including one soliton two soliton solution are obtained in addition on the basis of the three wave interaction model with self consistent sources we obtain the generation of second harmonics with self consistent sources

nest representations and dynamical systems abstract a nest representation is a generalized irreducible representation of a banach algebra on hubert space for a free discrete dynamical system every ideal in the semicrossed product algebra is equal to an intersection of kernels of nest representations a proper subset of all such kernels is a topological space homeomorphic to the space of all discrete finite arcs in the dynamical system with the subarc topology for certain continuous dynamical systems the corresponding set of kernels is isomorphic to the topological space of continuous finite arcs a banach algebra isomorphism of semicrossed products implies orbit order conjugacy of the underlying dynamical systems nest algebras and a non free action are also considered

primitive limit algebras and c envelopes in this paper we study irreducible representations of regular limit subalgebras of af algebras the main result is twofold every closed prime ideal of a limit of direct sums of nest algebras nsaf is primitive and every prime regular limit algebra is primitive a key step is that the quotient of an nsaf algebra by any closed ideal has an af c envelope and this algebra is exhibited as a quotient of a concretely represented af algebra when the ideal is prime the c envelope is primitive the gns construction is used to produce algebraically irreducible in fact n transitive for all n 1 representations for quotients of nsaf algebras by closed prime ideals thus the closed prime ideals of nsaf algebras coincide with the primitive ideals moreover these representations extend to representations of the c envelope of the quotient so that a fortiori these algebras are also operator primitive the same holds true for arbitrary limit algebras and the 0 ideal

elgenvalues of nonnegative matrices abstract in a partial continuation of work by fiedler some spectral properties of symmetric nonnegative matrices are extended to general nonnegative matrices

some types of solutions and generalized binary darboux transformation for the mkp equation with self consistent sources in this paper an mkp equation with self consistent sources mkpescss is structured in the framework of the constrained mkp equation based on the conjugate lax pairs we construct the generalized binary darboux transformation and the n times repeated darboux transformation with arbitrary functions at time t for the mkpescss which offers a non auto backlund transformation between two mkpescss with different degrees of sources with the help of these transformations some new solutions for the mkpescss such as soliton solutions rational solutions breather type solutions and exponential solutions are found by taking the special initial solution for auxiliary linear problems and the special functions of t time

power series with positive coefficients arising from the characteristic polynomials of positive matrices let a be an n times n entrywise positive matrix and let f t det i t a we prove the surprising result that there always exists a positive integer n such that the formal power series expansion of 1 f t 1 n around t 0 has positive coefficients

the spectra of nonnegative integer matrices via formal power series an old problem in matrix theory is to determine the n tuples of complex numbers which can occur as the spectrum of a matrix with nonnegative entries see bp94 chapter 4 or min88 chapter vii authors have studied the case where the ntuple is comprised of real numbers bor95 cia68 fri78 kel71 per53 sal72 sou83 sul49 the case where the matrices under consideration are symmetric fie74 jll96 and the general problem joh81 lm99 ll79 rea94 rea96 wuw97 various necessary conditions and sufficient conditions have been provided but a complete characterization is known for real n tuples only for n 4 kel71 sul49 and for complex n tuples only for n 3 ll79 motivated by symbolic dynamics boyle and handelman refocused attention on the nonzero part of the spectrum by making the following spectral conjecture bh91 bh93 see also boy93 8 and lm95 chapter 11 below a matrix a is primitive if all entries of a are nonnegative and for some n all entries of a are strictly positive also

2d toda lattice equation with self consistent sources casoratian type solutions bilinear backlund transformation and lax pair the two dimensional toda lattice equation with self consistent sources is proposed based on its bilinear forms casoratian type solutions and backlund transformation bt for the bilinear forms are presented starting from the bt a lax pair is derived for the 2d toda lattice with self consistent sources

triangular uhf algebras in this paper we classify triangular uhf algebras the generic triangular uhf algebra is constructed as follows let pn be any sequence of positive integers such that pm pn whenever m n for each n let tpn be the algebra of all pn pn upper triangular complex matrices and for m n let pn pm tpm tpn be the mapping x 1d x where d pnpm a triangular uhf algebra tuhf of rank pn is any banach algebra that is isometrically isomorphic to the banach algebra inductive limit t limn tpn pm the principal result of the paper is that if j and t are arbitrary tuhf algebras then j is isometrically isomorphic to t if and only if j and t have the same supernatural number

tensor algebras of c correspondences and their c envelopes abstract we show that the c envelope of the tensor algebra of an arbitrary c correspondence x coincides with the cuntz pimsner algebra o x as defined by katsura t katsura on c algebras associated with c correspondences j funct anal 217 2004 366 401 this improves earlier results of muhly and solel p s muhly b solel tensor algebras over c correspondences representations dilations and c envelopes j funct anal 158 1998 389 457 and fowler muhly and raeburn n fowler p muhly i raeburn representations of cuntz pimsner algebras indiana univ math j 52 2003 569 605 who came to the same conclusion under the additional hypothesis that x is strict and faithful

a characterization of trace zero nonnegative 5 5 matrices let 1 2 3 4 5 be a list of complex numbers with 1 2 3 4 5 0 necessary and sufficient conditions for the existence of an entry wise nonnegative 5 5 matrix a with spectrum are presented

the exact solutions to a ragnisco tu hierarchy with self consistent sources abstract the ragnisco tu hierarchy with self consistent sources is derived the exact solutions of the hierarchy are obtained via the inverse scattering transform ist an explicit form for a solution of the ragnisco tu equation is presented

bilinear backlund transformation for the kdv equation with a source a bilinear backlund transformation for the kdv equation with a source is obtained by using the bilinear transformation method superposition formulae for solutions are then constructed which satisfy bianchi s exchange property and it is shown that they have a simple structure when they are written in the bilinear forms the inverse scattering transform for the equation is also derived from the backlund transformation

approximately finitely acting operator algebras let e be an operator algebra on a hilbert space with finite dimensional c algebra c e a classification is given of the locally finite algebras a0 formula ak k and the operator algebras a formula ak k obtained as limits of direct sums of matrix algebras over e with respect to star extendible homomorphisms the invariants in the algebraic case consist of an additive semigroup with scale which is a right module for the semiring ve homu e e of unitary equivalence classes of star extendible homomorphisms this semigroup is referred to as the dimension module invariant in the operator algebra case the invariants consist of a metrized additive semigroup with scale and a contractive right module ve action subcategories of algebras determined by restricted classes of embeddings such as 1 decomposable embeddings between digraph algebras are also classified in terms of simplified dimension modules

realizable lists on a class of nonnegative matrices abstract a square matrix of order n with n 2 is called permutative matrix when all its rows are permutations of the first row in this paper recalling spectral results for partitioned into 2 by 2 symmetric blocks matrices sufficient conditions on a given complex list to be the list of the eigenvalues of a nonnegative permutative matrix are given in particular we study niep and pniep when some complex elements in the lists under consideration have non zero imaginary part realizability regions for nonnegative permutative matrices are obtained a guo s realizability preserving perturbations result is obtained

operator algebras and subproduct systems arising from stochastic matrices we study subproduct systems in the sense of shalit and solel arising from stochastic matrices on countable state spaces and their associated operator algebras we focus on the non self adjoint tensor algebra and viselter s generalization of the cuntz pimsner c algebra to the context of subproduct systems suppose that x and y are arveson stinespring subproduct systems associated to two stochastic matrices over a countable set and let t x and t y be their tensor algebras we show that every algebraic isomorphism from t x onto t y is automatically bounded furthermore t x and t y are isometrically isomorphic if and only if x and y are unitarily isomorphic up to a automorphism of l when is finite we prove that t x and t y are algebraically isomorphic if and only if there exists a similarity between x and y up to a automorphism of l moreover we provide an explicit description of the cuntz pimsner algebra o x in the case where is finite and the stochastic matrix is essential

algebraic isomorphisms of limit algebras we prove that algebraic isomorphisms between limit algebras are automatically continuous and consider the consequences of this result in particular we give partial solutions to a conjecture and an open problem by power as a further consequence we describe epimorphisms between various classes of limit algebras in this paper we study automatic continuity for limit algebras automatic continuity involves algebraic conditions on a linear operator from one banach algebra into another that guarantee the norm continuity of the operator this is a generalization via the open mapping theorem of the uniqueness of norms problem recall that a banach algebra a is said to have a unique banach algebra topology if any two complete algebra norms on a are equivalent so that the norm topology determined by a banach algebra is unique uniqueness of norms automatic continuity and related questions have played an important and long standing role in the theory of banach algebras 6 29 28 10 11 2 limit algebras whose theory has grown rapidly in recent years are the nonselfadjoint analogues of uhf and af c algebras we first prove that algebraic isomorphisms between limit algebras are automatically continuous theorem 1 4 this proof uses the ideal theory of limit algebras as well as key results from the theory of automatic continuity for banach algebras combining this with 23 theorem 8 3 verifies power s conjecture that the c envelope of a limit algebra is an invariant for purely algebraic isomorphisms for limits of finite dimensional nest algebras and in particular for all triangular limit algebras corollary 1 6 in 5 the first two authors studied triangular limit algebras in terms of their lattices of ideals by combining automatic continuity with this work we show that within the class of algebras generated by their order preserving normalizers see below for definitions algebraically isomorphic algebras are isometrically isomorphic theorem 2 5 this shows that the spectrum or fundamental relation 20 a topological binary relation which provides coordinates for limit algebras and is a useful tool in classifications is a complete algebraic isomorphism invariant for this class corollary 2 6 in recent work the second two authors studied primitivity for limit algebras 9 showing that a variety of limit algebras are primitive these results together with automatic continuity give descriptions of epimorphisms between various classes of limit algebras namely lexicographic algebras theorem 3 2 and z analytic algebras theorem 3 3 received by the editors april 6 1998 and in revised form october 7 1999 2000 mathematics subject classification primary 47d25 46k50 46h40 research partially supported by an nsf grant 2000 american mathematical society

structure of free semigroupoid algebras abstract a free semigroupoid algebra is the wot closure of the algebra generated by a tck family of a graph we obtain a structure theory for these algebras analogous to that of free semigroup algebra we clarify the role of absolute continuity and wandering vectors these results are applied to obtain a lebesgue von neumann wold decomposition of tck families along with reflexivity a kaplansky density theorem and classification for free semigroupoid algebras several classes of examples are discussed and developed including self adjoint examples and a classification of atomic free semigroupoid algebras up to unitary equivalence

the periodic solutions of the discrete modified kdv equation with a self consistent source abstract this work is devoted to the application of inverse spectral problem for integration of the periodic solutions of the discrete modified kdv equation with a self consistent source the effective method of solution of the inverse spectral problem for the discrete linear ablowitz ladik equation is presented

the lattice of ideals of a triangular af algebra we study triangular af taf algebras in terms of their lattices of closed two sided ideals not isometrically isomorphic taf algebras can have isomorphic lattices of ideals indeed there is an uncountable family of pairwise non isomorphic algebras all with isomorphic lattices of ideals in the positive direction if a and b are strongly maximal taf algebras with isomorphic lattices of ideals then there is a bijective isometry between the subalgebras of a and b generated by their order preserving normalizers this bijective isometry is the sum of an algebra isomorphism and an anti isomorphism using this we show that if the taf algebras are generated by their order preserving normalizers and are triangular subalgebras of primitive c algebras then the lattices of ideals are isomorphic if and only if the algebras are either isometrically isomorphic or anti isomorphic finally we use complete distributivity to show that there are taf algebras whose 0 lattices of ideals can not arise from taf algebras generated by their order preserving 8 normalizers our techniques rely on constructing a topological binary relation based on the lattice of ideals this relation is closely connected to the spectrum or fundamental relation also a topological binary relation of the taf algebra

on the nonnegative eigenvalue problem abstract 1 1 n is the spectrum of a stochastic matrix of order n 1 if and only if there exists some real matrix b of order n with spectrum 1 n and some n simplex s r n containing the origin such that bs s this result appears implicitly in ciarlet s work and it provides us with a geometrical tool to obtain sufficient conditions for the nonnegative eigenvalue problem we employ it here to generalize the sufficient conditions given by kellogg

strong shift equivalence and the generalized spectral conjecture for nonnegative matrices abstract given matrices a and b shift equivalent over a dense subring r of r with a primitive we show that b is strong shift equivalent over r to a primitive matrix this result shows that the weak form of the generalized spectral conjecture for primitive matrices implies the strong form the foundation of this work is the recent result that for any ring r the group nk 1 r of algebraic k theory classifies the refinement of shift equivalence by strong shift equivalence for matrices over r

operator algebras of monomial ideals in noncommuting variables abstract we study operator algebras arising from monomial ideals in the ring of polynomials in noncommuting variables through the apparatus of subproduct systems and c correspondences we provide a full comparison amongst the related operator algebras for our analysis we isolate a partially defined dynamical system to which we refer as the quantised dynamics of the monomial ideal in addition we revisit several previously considered constructions these include matsumoto s subshift c algebras as well as the tensor and the pimsner algebras associated with dynamical systems or graphs we sort out the various relations by giving concrete conditions and counterexamples that orientate the operator algebras of our context it appears that the boundary c algebras do not arise as the quotient with the compact operators unconditionally we establish a dichotomy to this effect by examining the resulting tensor algebras we identify their boundary representations we analyse their c envelopes and we give criteria for hyperrigidity moreover we completely classify them in terms of the data provided by the monomial ideals for tensor algebras of c correspondences and bounded isomorphisms this is achieved up to the level of local conjugacy in the sense of davidson and roydor for the quantised dynamics for tensor algebras of subproduct systems and algebraic isomorphisms this is achieved up to the level of equality of monomial ideals modulo permutations of the variables in the process we accomplish more in different directions most notably we show that tensor algebras form a complete invariant for isomorphic resp similar subproduct systems of homogeneous ideals up to isometric resp bounded isomorphisms the results on local conjugacy are obtained via an alternative proof of the breakthrough result of davidson and katsoulis on piecewise conjugate systems for our purposes we use appropriate compressions of the fock representation we then apply this alternative proof locally for the partially defined quantised dynamics in this way we avoid the topological graphs machinery and pave the way for further applications these include operator algebras of dynamical systems over commuting contractions or over row commuting contractions

nest representations of directed graph algebras this paper is a comprehensive study of the nest representations for the free semigroupoid algebra mathfrak l g of a countable directed graph g as well as its norm closed counterpart the tensor algebra mathcal t g we prove that the finite dimensional nest representations separate the points in mathfrak l g and a fortiori in mathcal t g the irreducible finite dimensional representations separate the points in mathfrak l g if and only if g is transitive in components which is equivalent to being semisimple also the upper triangular nest representations separate points if and only if for every vertex x in mathcal t g supporting a cycle x also supports at least one loop edge we also study faithful nest representations we prove that mathfrak l g or mathcal t g admits a faithful irreducible representation if and only if g is strongly transitive as a directed graph more generally we obtain a condition on g which is equivalent to the existence of a faithful nest representation we also give a condition that determines the existence of a faithful nest representation for a maximal type mathbb n nest

integrability of the semi discrete toda equation with self consistent sources a new procedure to construct and solve soliton equations with self consistent sources sescss is applied to the semi discrete toda equation based on its bilinear from bilinear backlund transformation bt for the semi discrete toda escs is presented starting from the bt a lax pair is derived for the semi discrete toda escs

the real nonnegative inverse eigenvalue problem is np hard abstract a list of complex numbers is realizable if it is the spectrum of a nonnegative matrix in 1949 suleimanova posed the nonnegative inverse eigenvalue problem niep the problem of determining which lists of complex numbers are realizable the version for reals of the niep rniep asks for realizable lists of real numbers in the literature there are many sufficient conditions or criteria for lists of real numbers to be realizable we will present an unified account of these criteria then we will see that the decision problem associated to the rniep is np hard and we will study the complexity for the decision problems associated to known criteria

on the toda lattice equation with self consistent sources the toda lattice hierarchy with self consistent sources and their lax representation are derived we construct a forward darboux transformation fdt with arbitrary functions of time and a generalized forward darboux transformation gfdt for toda lattice with self consistent sources tlscs which can serve as a non auto backlund transformation between tlscs with different degrees of sources with the help of such dt we can construct many types of solutions to tlscs such as rational solution solitons positons negetons and soliton positons soliton negatons positon negatons etc and study properties and interactions of these solutions

primitive triangular uhf algebras abstract we prove that a large class of triangular uhf algebras are primitive we use two avenues to obtain our results a direct approach in which we explicitly construct a faithful algebraically irreducible representation of the algebra on a separable hilbert space as well as an indirect algebraic approach which utilizes the prime ideal structure of the algebra using these results we completely characterize the primitive ideal spaces of all lexicographic algebras an ideal there is primitive if and only if it is closed prime specializing on the algebras a q we obtain a complete classification of their algebraic isomorphisms and epimorphisms through the use of a new invariant involving the primitive ideal space finally we characterize the primitive ideal spaces of z analytic and order preserving algebras and obtain information about their epimorphisms

hardy algebras w correspondences and interpolation theory given a von neumann algebra m and a w correspondence e over m we construct an algebra h e that we call the hardy algebra of e when m open image in new window e h e is the classical hardy space h open image in new window of bounded analytic functions on the unit disc when m open image in new window and e open image in new window h e is the free semigroup algebra studied by popescu davidson and pitts and many others we show that given any faithful normal representation of m on a hilbert space h there is a natural correspondence e over the commutant m called the dual of e and that h e can be realized in terms of b h valued functions on the open unit ball open image in new window e in the space of adjoints of elements in e we prove analogues of the nevanlinna pick theorem in this setting and discover other aspects of the value distribution theory for elements in h e we also analyze the boundary behavior of elements in h e and obtain generalizations of the sz nagy foias functional calculus and the functional calculus of popescu for c n c row contractions the correspondence e has a dual that is naturally isomorphic to e and the commutants of certain so called induced representations of h e can be viewed as induced representations of h e for these induced representations a double commutant theorem is proved

isomorphisms between topological conjugacy algebras a family of algebras which we call topological conjugacy algebras is associated with each proper continuous map on a locally compact hausdorff space assume that i xi xi is a continuous proper map on a locally compact hausdorff space xi for i 1 2 we show that the dynamical systems x1 1 and x2 2 are conjugate if and only if some topological conjugacy algebra of x1 1 is isomorphic as an algebra to some topological conjugacy algebra of x2 2 this implies as a corollary the complete classification of the semicrossed products c0 x z which was previously considered by arveson and josephson 3 peters 19 hadwin and hoover 8 and power 21 we also obtain a complete classification of all semicrossed products of the form a d z where a d denotes the disc algebra and d d a continuous map which is analytic on the interior in this case a surprising dichotomy appears in the classification scheme which depends on the fixed point set of we also classify more general semicrossed products of uniform algebras

on the pfaffianized kp equation with self consistent sources abstract a new procedure called source generation is applied to the pfaffianized kp equation as a result the pfaffianized kp equation with self consistent sources escs is obtained this coupled system cannot only be reduced to the pfaffianized kp equation but also reduced to the kp equation with self consistent sources kpescs so the pfaffianized kp escs can be viewed as a pfaffian version of the kpescs which indicates the commutativity of the source generation procedure and pfaffianization

small polynomial matrix presentations of nonnegative matrices we investigate the use of polynomial matrices to give efficient presentations of nonnegative matrices exhibiting prescribed spectral and algebraic behavior

on the non isospectral kadomtsev petviashvili equation with self consistent sources abstract a new procedure called source generation is applied to construct non isospectral soliton equations with self consistent sources as results the non isospectral kadomtsev petviashvili equation with self consistent sources kpescs and its gramm type determinant solutions are obtained furthermore the non isospectral pfaffianized kp equation with self consistent sources is constructed this coupled system can not only be reduced to the non isospectral pfaffianized kp equation but also reduced to the non isospectral kpescs

operator algebras associated with unitary commutation relations abstract we define nonselfadjoint operator algebras with generators l e 1 l e n l f 1 l f m subject to the unitary commutation relations of the form l e i l f j k l u i j k l l f l l e k where u u i j k l is an n m n m unitary matrix these algebras which generalise the analytic toeplitz algebras of rank 2 graphs with a single vertex are classified up to isometric isomorphism in terms of the matrix u

circle actions on c algebras partial automorphisms and a generalized pimsner voiculescu exact sequence abstract we introduce a method to study c algebras possessing an action of the circle group from the point of view of their internal structure and their k theory under relatively mild conditions our structure theorem shows that any c algebra where an action of the circle is given arises as the result of a construction that generalizes crossed products by the group of integers such a generalized crossed product construction is carried out for any partial automorphism of a c algebra where by a partial automorphism we mean an isomorphism between two ideals of the given algebra our second main result is an extension to crossed products by partial automorphisms of the celebrated pimsner voiculescu exact sequence for k groups the representation theory of the algebra arising from our construction is shown to parallel the representation theory for c dynamical systems in particular we generalize several of the main results relating to regular and covariant representations of crossed products

applications of the wold decomposition to the study of row contractions associated with directed graphs based on a wold decomposition for families of partial isometries and projections of cuntz krieger toeplitz type we extend several fundamental theorems from the case of single vertex graphs to the general case of countable directed graphs with no sinks we prove a szego type factorization theorem for ckt families which leads to information on the structure of the unit ball in free semigroupoid algebras and show that joint similarity implies joint unitary equivalence for such families for each graph we prove a generalization of von neumann s inequality which applies to row contractions of operators on hilbert space which are related to the graph in a natural way this yields a functional calculus determined by quiver algebras and free semigroupoid algebras we establish a generalization of coburn s theorem for the c algebra of a ckt family and prove a universality theorem for c algebras generated by these families in both cases the c algebras generated by quiver algebras play the universal role

an equivariant brauer group and actions of groups onc algebras suppose that g t is a second countable locally compact trans formation group given by a homomorphism l g homeo t and that a is a separable continuous trace c algebra with spectrum t an action g aut a is said to cover l if the induced action of g on t coincides with the original one we prove that the set brg t of morita equivalence classes of such systems forms a group with multiplication given by the balanced tensor product a b a c0 t b and we refer to brg t as the equivariant brauer group we give a detailed analysis of the structure of brg t in terms of the moore cohomology of the group g and the integral cohomology of the space t using this we can characterize the stable continuous trace c algebras with spectrum t which admit actions covering l in particular we prove that if g r then every stable continuous trace c algebra admits an essentially unique action covering l thereby substantially improving results of raeburn and rosenberg

structured triangular limit algebras we investigate a class of triangular uhf algebras which have the special property that there exists a sequence of unital multiplicative contractive finite rank conditional expectations of the algebra into itself which converges strongly to the identity whose ranges form an increasing chain with dense union a partial classification is given in terms of a local finiteness property and a delimiting counterexample is obtained associated inverse limit algebras are considered and a characterization of residually finite dimensional triangular af algebras is obtained 1991 mathematics subject classification 47d25 46j35

on positive matrices abstract we relate several results on positive matrices due to soittola 1976 handelman 1981 1987 and lind 1984 giving conditions for the existence of some positive matrix to represent a linear map the result of soittola concerns finite automata and those of handelman and lind concern symbolic dynamics

the non isospectral modified kadomtsev petviashvili equation with self consistent sources and its coupled system abstract a new algebraic method called source generation procedure is applied to construct non isospectral soliton equations with self consistent sources as results the non isospectral modified kadomtsev petviashvili equation with self consistent sources mkpescs and its gramm type determinant solutions are obtained by using the source generation procedure furthermore a new coupled system of the non isospectral mkpescs and its pfaffian solutions are constructed

on the ablowitz ladik equations with self consistent sources darboux transformations and explicit solutions to ablowitz ladik al equations with self consistent sources alescs are studied based on the darboux transformation dt for the al problem we construct three types of non auto backlund transformations connected with al systems with different numbers of sources the degenerate cases of dt and their applications to the reduced systems of alescs for instance discrete nonlinear schrodinger with self consistent sources d nlsscs and discrete mkdv equation with self consistent sources d mkdvscs are discussed many types of solutions of alescs d nlsscs and d mkdvscs including solitons positons negatons can be derived from dts and their degenerate cases

pfaffian solution of a semi discrete bkp type equation and its source generation version the pfaffian solution of a semi discrete bkp type equation is obtained at first then utilizing the source generation procedure this equation with self consistent sources bkpescs is presented and its pfaffian solutions are derived finally a bilinear backlund transformation for the semi discrete bkpescs is given

solution of an initial boundary value problem for coupled nonlinear waves the authors derive and study a hierarchy of nonlinear coupled evolution equations among which is the coupled korteveg de vries schrodinger equation for which they prove that a mixed initial boundary value problem is solvable they give the method of solution together with the backlund transformation and establish the infinite set of conserved densities they finally discuss the applicability of such equations in plasma physics and hydrodynamics

ideals in some continuous nonselfadjoint crossed product algebras abstract let y t be a locally compact dynamical system where the t denotes a continuous one parameter semigroup of maps on y when each t is a homeomorphism a nonselfadjoint crossed product algebra is defined as the subalgebra of the c crossed product c 0 y r supported on t 0 when each t is only continuous the crossed product c 0 y r can still be defined the ideal structure of such an algebra is determined in the case where the semigroup action is the suspension of a discrete free action on a smaller space x a generalization of effros hahn is given whereby one may find a meet irreducible ideal over any arc closure in y the meet irreducible ideals form a topological space in the hull kernel topology and there is a one to one correspondence between closed sets in this space and closed ideals in the algebra a subset of this space is homeomorphic to the space of finite arcs in the subarc topology the irrational flow algebra is considered as a special case