algebraic reflexivity of sets of bounded operators on vector valued lipschitz functions abstract in this paper we establish algebraic reflexivity properties of subsets of bounded linear operators acting on spaces of vector valued lipschitz functions we also derive a representation for the generalized bi circular projections on these spaces

completely rank nonincreasing linear maps abstract we give purely algebraic characterizations of the maps that are approximate compressions or skew compressions of a unital representation of a c algebra the key techniques used also relate to closures of joint similarity orbits of matrices and elementary maps on b h

a note on isometries of lipschitz spaces abstract the main purpose of this article is to generalize a recent result about isometries of lipschitz spaces botelho fleming and jamison 2 described surjective linear isometries between vector valued lipschitz spaces under certain conditions in this article we extend the main result of 2 by removing the quasi sub reflexivity condition from banach spaces

applications of riordan matrix functions to bernoulli and euler polynomials abstract we define riordan matrix functions associated with riordan arrays and study their algebraic properties we also give their applications in the construction of new classes of bernoulli and euler polynomials and bernoulli and euler numbers referred to as the duals and conjugate bernoulli and euler polynomials and dual and conjugate bernoulli and euler numbers respectively

minimal locally linearly dependent spaces of operators abstract let s be an n dimensional minimal locally linearly dependent space of operators acting between vector spaces u and v we obtain the sharp lower bound and the sharp upper bound for dim s u and give a complete description of those minimal locally linearly dependent spaces at which the upper bound is attained

homomorphisms between algebras of lipschitz functions with the values in function algebras abstract we give a characterization of algebra homomorphisms and isomorphisms between banach algebras of lipschitz functions with the values in unital commutative c algebras we prove that such homomorphisms are composition operators of the form and preserve some properties

algebraic reflexivity of some subsets of the isometry group let x be a compact first countable space in this paper we show that the set of isometries of c x that are involutions is algebraically reflexive as a consequence of a recent work of botelho and jamison this leads to the conclusion that the set of generalized bi circular projections on c x is also algebraically reflexive we also consider these questions for the space c x e where e is a uniformly convex banach space

algebraic reflexivity of the isometry group of some spaces of lipschitz functions abstract we show that the isometry groups of lip x d and lip x d with 0 1 for a compact metric space x d are algebraically reflexive we also prove that the sets of isometric reflections and generalized bi circular projections on such spaces are algebraically reflexive in order to achieve this we characterize generalized bi circular projections on these spaces

local automorphisms of nest subalgebras of factor von neumann algebras in this paper it is proved that every surjective weakly continuous linear local automorphism of nest subalgebras with non trivial nests of factor von neumann algebras is an automorphism and that every surjective linear 2 local automorphism of nest algebras with non trivial nests of factor von neumann algebras is an automorphism

extreme points and isometries on vector valued lipschitz spaces abstract for a banach space e and a compact metric space x d a function f x e is a lipschitz function if there exists k 0 such that f x f y k d x y for all x y x the smallest such k is called the lipschitz constant l f for f the space lip x e of all lipschitz functions from x to e is a banach space under the norm defined by f max l f f where f sup f x x x recent results characterizing isometries on these vector valued lipschitz spaces require the banach space e to be strictly convex we investigate the nature of the extreme points of the dual ball for lip x e and use the information to describe the surjective isometries on lip x e under certain conditions on e where e is not assumed to be strictly convex we make use of an embedding of lip x e into a space of continuous vector valued functions on a certain compact set

hyper tauberian algebras and weak amenability of figa talamanca herz algebras abstract we study certain commutative regular semisimple banach algebras which we call hyper tauberian algebras we first show that they form a subclass of weakly amenable tauberian algebras then we investigate the basic and hereditary properties of them moreover we show that if a is a hyper tauberian algebra then the linear space of bounded derivations from a into any banach a bimodule is reflexive we apply these results to the figa talamanca herz algebra a p g of a locally compact group g for p 1 we show that a p g is hyper tauberian if the principal component of g is abelian finally by considering the quantization of these results we show that for any locally compact group g a p g equipped with an appropriate operator space structure is a quantized hyper tauberian algebra this in particular implies that a p g is operator weakly amenable

elliptic hypergeometric series on root systems abstract we derive a number of summation and transformation formulas for elliptic hypergeometric series on the root systems a n c n and d n in the special cases of classical and q series our approach leads to new elementary proofs of the corresponding identities

local derivations of nest subalgebras of von neumann algebras in this paper it is proved that every norm continuous linear local derivation of a nest subalgebra of a factor von neumann algebra is a derivation and that every linear 2 local derivation of a nest subalgebra of a factor von neumann algebra is a derivation

local derivations on certain csl algebras in this paper it is shown that every norm continuous linear local derivation from an arbitrary csl algebra whose lattice is generated by finitely many independent nests into any ultraweakly closed subalgebra which contains the algebra is an inner derivation and that every norm continuous linear local derivation from an arbitrary csl algebra whose lattice is completely distributive into any ultraweakly closed subalgebra which contains the algebra is a derivation

the elements of finite order in the riordan group over the complex field abstract an element of finite order in the riordan group over the real field must have order 1 or 2 if we extend all the entries to be complex numbers then it may have any finite order in the present paper we investigate the elements of finite order of the riordan group over the complex field this notion leads us to define an element of pseudo order k 2 and k pseudo involution respectively it turns out that the inverse of a k pseudo involution only differs from it in signs we clarify some relationship between the elements of pseudo order k and k pseudo involutions in particular k pseudo involutions for k 0 mod 4 are characterized by a single sequence the subgroups of the riordan group formed by the elements having pseudo order of a prime power p r are also introduced

comment on barut girardello and klauder perelomov coherent states for the kravchuk functions j math phys 48 112106 2007 we call attention to the misconstructions in a paper recently published in this journal a chenaghlou and o faizy j math phys 48 112106 2007 it is shown that the constructed barut girardello coherent states are problematic from the view points of the definition and the measure the claimed coherencies for the kravchuk functions cannot actually exist

riordan arrays generalized narayana triangles and series reversion abstract using elements of the group of riordan arrays we define a family of generalized narayana triangles and their associated generalized catalan numbers and study their links to series reversion in particular we use lagrange inversion techniques to determine the generating functions for these generalized catalan numbers

local isometries of function spaces abstract we show that for a large class of function spaces any isometry that coincides locally with a surjective isometry must be automatically surjective this class includes finite codimensional subspaces of c left x right and spaces c left x e right of e valued continuous functions for finite dimensional or uniformly convex and algebraically reflexive e

local derivations on operator algebras abstract when attempting to find sufficient conditions for a linear mapping to be a derivation an obvious candidate is the concept of a local derivation local derivations on operator algebras have been investigated in recent papers of kadison j algebra130 1990 494 509 and larson and sourour proc symp pure math 51 1990 187 194 a local derivation is a norm continuous linear map from an operator algebra a into an a bimodule m which agrees with some derivation at each point in the algebra we show that if a is the direct limit of finite dimensional csl algebras via extendable embeddings e g a triangular af algebra then a local derivation on a must be a derivation further we show that for many finite dimensional operator algebras any inner local derivation must be an inner derivation

additive maps preserving jordan zero products on nest algebras abstract let alg n and alg m be nest algebras associated with the nests n and m on banach spaces assume that n n and m m are complemented whenever n n and m m let alg n alg m be a unital additive surjection it is shown that preserves jordan zero products in both directions that is a b b a 0 ab ba 0 if and only if is either a ring isomorphism or a ring anti isomorphism particularly all unital additive surjective maps between hilbert space nest algebras which preserves jordan zero products are characterized completely

a formula to construct all involutions in riordan matrix groups abstract we get a formula for all finite riordan involutions using the natural approximation induced by the inverse limit construction we also describe all infinite riordan matrices which are involutions in the riordan group finally we get some consequences

rank one operators and bimodules of reflexive operator algebras in banach spaces abstract in this paper we give some results concerning reflexive operator algebras in banach spaces first we prove that if a is a nest algebra xi x a a and e 0 are given then there exists an operator f which equals the sum of two operators of rank at most one in the nest algebra such that axi fxi m of a reflexive operator algebra a such that lat a is completely distributive and m a the commutant c a m of a modulo m equals m particularly this is true for nest algebras

riordan group involutions we study involutions in the riordan group especially those with combinatorial meaning we give a new determinantal criterion for a matrix to be a riordan involution and examine several classes of examples a complete characterization of involutions in the appell subgroup is developed in another direction we find several examples that generalize the rna matrix but are of independent interest

hyperreflexivity of finite dimensional subspaces we show that each reflexive finite dimensional subspace of operators is hyperreflexive this gives a positive answer to a problem of kraus and larson we also show that each n dimensional subspace of hilbert space operators is 2n hyperreflexive

riordan arrays and d orthogonality abstract using the theory of the riordan group and d orthogonal polynomials we shall show that sequences of d orthogonal polynomials can be also generated by the riordan group we interpret some families of d orthogonal polynomials within the framework of the riordan group

on 2 local isometries on continuous vector valued function spaces article history received 24 july 2008 available online 24 december 2008 submitted by j d m wright a not necessarily linear mapping from a banach space x to a banach space y is said to be a 2 local isometry if for any pair x y of elements of x t here is as urjective linear isometry t x y such that tx x and ty y we show that under certain conditions on locally compact hausdorff spaces q k and a banach space e e very 2 local isometry on c0 q e to c0 k e is linear and surjective we also show that every 2 local isometry on p is linear and surjective for 1 p p 2 but this fails for the hilbert space 2

simple proofs of open problems about the structure of involutions in the riordan group abstract we prove that if d g x f x is an element of order 2 in the riordan group then g x exp x xf x for some antisymmetric function x z also we prove that every element of order 2 in the riordan group can be written as bmb 1 for some element b and m 1 1 in the riordan group these proofs provide solutions to two open problems presented by l shapiro l w shapiro some open questions about random walks involutions limiting distributions and generating functions adv appl math 27 2001 585 596

hermitian operators and isometries on injective tensor products of uniform algebras and c algebras abstract we describe the general form of a hermitian operator on the injective tensor product of a uniform algebra and a complex banach space as an application we characterize a surjective unital isometry between the injective tensor product of a uniform algebra and a unital factor c algebra in particular we give a simple proof that a unital factor c algebra has the banach stone property

representing polynomials as characteristic polynomials via the stieltjes transform abstract the stieltjes transform s a of an infinite lower triangular matrix a with nonzero diagonal entries is defined by s a a 1 a where a is the matrix obtained from a by deleting its initial row in this paper we express a sequence of polynomials as the characteristic polynomials of the stieltjes transforms using a highly structured infinite lower triangular matrix called a riordan matrix as a result computation of the zeros of such polynomials becomes amenable to iterative methods for computing eigenvalues or to eigenvalue location theorems such as the gersgorin theorem we also describe a finite analog of the polynomial correspondence and its relationship to eigenvalue regions as an application the recurrence relations for several polynomial sequences are obtained using the stieltjes transform

hyperreflexivity of the derivation space of some group algebras let t be a continuous linear operator on a banach algebra a we address the question of whether the constant rm sup at b c a b c in a ab bc 0 a b c 1 being small implies that the distance from t to the space der a of all continuous derivations on a is small we show that this is the case for amenable group algebras as a consequence we deduce that der l 1 g is hyperreflexive for each amenable group in sin

separating vectors and reflexivity abstract there is a close connection between separating vectors and reflexivity but the existence of a separating vector does not guarantee reflexivity this paper clarifies the relation we first find that every subspace of linear transformations whose dimension is less than the cardinality of the scalar field and having a disjoint pair of separating vectors is algebraically reflexive then we refine the result and conclude that a finite dimensional subspace of operators having a two dimensional subspace of separating vectors is algebraically reflexive if its scalar field is algebraically closed examples are provided to show that these results are sharp an application of the first result shows that finite dimensional spaces of operators of large rank are reflexive

matrix factorization of the n n shift bell matrix abstract let b n b n k n k 0 be the bell matrix define the n n shift bell matrix p n k by p n k i j b k i 1 k j 1 for i j 1 2 n and k 0 1 2 in this paper matrix factorizations of the n n shift bell matrix and the n n generalized riordan matrix are studied as a result many lower triangular matrices related to bell polynomials can be factorized by the corresponding matrices and some identities are derived from the matrix representations in addition some harmonic number identities are obtained from the riordan array method

coherent states even and odd coherent states in a finite dimensional hilbert space and their properties we have considered a harmonic oscillator in a finite dimensional hilbert space spanned by orthogonal polynomials of a discrete variable and constructed coherent states as well as even and odd coherent states of this oscillator various properties such as squeezing and antibunching of these states have also been examined

local isometries on spaces of continuous functions let x and y be banach spaces and s a subset of the space of linear continuous operators from x to y we say that an operator t belongs locally to s if for every x x there is s s possibly depending on x such that tx sx pointwise should be better than locally but we have followed tradition if each operator that belongs locally to s belongs in fact to s we say that s is algebraically reflexive when y x and s iso x is the group of isometries of x we say that t is a local isometry of x in this paper isometry means linear surjective isometry similarly a local automorphism of a banach algebra is an operator which agrees at every point with some automorphism also we will consider approximate local isometries and automorphisms these are operators having with the following property given x x and e 0 there is an isometry respectively an automorphism s of x such that tx sx e the study of local isometries and automorphisms of banach algebras spurred a considerable interest in recent years see the bibliography of the dissertation 16 in this paper we deal with local isometries and automorphisms of the algebras c0 l as usual we write c0 l or c k 0 l for the banach algebra of all continuous k valued functions on the locally compact space l vanishing at infinity where k is either c or r if l is compact the subscript will be omitted by the banach stone theorem if t is local isometry of c0 l then for each f there are a homeomorphism of l and a continuous unitary u l k such that tf u f

on the completeness of coherent states generated by binomial distribution we demonstrate the completeness of boson and spin coherent states generated by binomial distribution by furnishing the exact analytical form of their respective positive weight functions in resolution of unity these weight functions are solutions of the associated truncated stieltjes power moment problem we elaborate on the non unique character of these solutions

locally linearly dependent operators and reflexivity of operator spaces we obtain two results on the existence of large subspaces of operators of small rank in locally linearly dependent spaces of operators as a consequence we obtain an upper bound for the rank of operators belonging to a minimal locally linearly dependent space of operators it has been known that the only obstruction to the reflexivity of a finite dimensional operator space comes from the operators with small ranks our results improve known bounds on the minimal rank that guarantees the reflexivity

on the relative reflexivity of finitely generated modules of operators let s be a von neumann algebra on a hilbert space z with commutant and centre w for each subspace e of s let ref r be the space of all b e w such that xby 0 for all x y e s satisfying xyy o if ref y the space y is called s reflexive if s z and 5 is an algebra containing the identity operator s reflexivity reduces to the usual reflexivity in operator theory the main result of the paper is the following if y is one dimensional or if r is arbitrary finitedimensional but s has no central portions of type in for n 1 then the space is s reflexive and the space is z reflexive where the bar denotes the closure in the ultraweak operator topology if s is a factor then is closed in the weak operator topology for each finite dimensional subspace 5 of s

corrigendum to hermitian operators on banach algebras of vector valued lipschitz maps j math anal appl 452 2017 378 387 abstract the purpose of the paper it to correct theorem 11 in 1 and give a precise proof

mertens equimodular matrices of redheffer type abstract asymptotic behavior of the mertens function m n k 0 n k which is equal to the determinant of the n n redheffer matrix is known to be closely related to the riemann hypothesis an infinite matrix whose nth leading principal minor is equal to m n for all n 1 is called a mertens equimodular matrix we use riordan matrices to find a large class of mertens equimodular matrices each element of which is called by us a riordan redheffer matrix briefly an r r matrix we also give the generating function for the characteristic polynomials of r r matrices as a result we introduce several examples of r r matrices that reveal interesting spectral properties further we pose two conjectures on the eigenvalues of those r r matrices finally we find a sufficient condition for the riemann hypothesis using the smallest singular value of a r r matrix

2 local automorphisms of operator algebras abstract a not necessarily continuous linear or multiplicative function from an algebra a into itself is called a 2 local automorphism if agrees with an automorphism of a at each pair of points in a in this paper we study when a 2 local automorphism of a c algebra or a standard operator algebra on a locally convex space is an automorphism

shift operators defined in the riordan group and their applications abstract in this paper we discuss a linear operator t defined in riordan group r by using the upper shift matrix u and lower shift matrix u t namely for each r r t r u r u t some isomorphic properties of the operator t and the structures of its range sets for different domains are studied by using the operator t and the properties of bell subgroup of r the riordan type chu vandermonde identities and the riordan equivalent identities of format last theorem and beal conjecture are shown the applications of the shift operators to the complementary riordan arrays and to the riordan involutions and riordan pseudo involutions are also presented

symmetry classes of alternating sign matrices under one roof in a previous article math co 9712207 we derived the alternating sign matrix asm theorem from the izergin korepin determinant for a partition function for square ice with domain wall boundary here we show that the same argument enumerates three other symmetry classes of alternating sign matrices vsasms vertically symmetric asms even htsasms half turn symmetric asms and even qtsasms quarter turn symmetric asms the vsasm enumeration was conjectured by mills the others by robbins math co 0008045 we introduce several new types of asms uasms asms with a u turn side uuasms two u turn sides osasms off diagonally symmetric asms oosasms off diagonally off antidiagonally symmetric and uosasms off diagonally symmetric with u turn sides uasms generalize vsasms while uuasms generalize vhsasms vertically and horizontally symmetric asms and another new class vhpasms vertically and horizontally perverse osasms oosasms and uosasms are related to the remaining symmetry classes of asms namely dsasms diagonally symmetric dasasms diagonally anti diagonally symmetric and tsasms totally symmetric asms we enumerate several of these new classes and we provide several 2 enumerations and 3 enumerations our main technical tool is a set of multi parameter determinant and pfaffian formulas generalizing the izergin korepin determinant for asms and the tsuchiya determinant for uasms solv int 9804010 we evaluate specializations of the determinants and pfaffians using the factor exhaustion method

algebraic reflexivity of isometry groups of algebras of lipschitz maps abstract we study groups of surjective linear isometries on banach algebras of lipschitz maps with values in some unital c algebras in this paper these spaces are endowed with the sum norm for the case where the c algebras are commutative whose groups of all surjective isometries are algebraically reflexive we prove that the group of all surjective isometries on the corresponding banach algebra of lipschitz maps are algebraically reflexive we also prove that the group of unital surjective isometries between matrix valued lipschitz algebras are reflexive

quantum cryptography without bell s theorem ekert has described a cryptographic scheme in which einstein podolsky rosen epr pairs of particles are used to generate identical random numbers in remote places while bell s theorem certifies that the particles have not been measured in transit by an eavesdropper we describe a related but simpler epr scheme and without invoking bell s theorem prove it secure against more general attacks including substitution of a fake epr source finally we show our scheme is equivalent to the original 1984 key distribution scheme of bennett and brassard which uses single particles instead of epr pairs

bounded reflexivity of kernels of elementary operators abstract kernels of elementary operators of length two give rise to many interesting classes of operators in this paper we study bounded reflexivity of these kernels for general banach spaces a sufficient condition is given for the kernels to be boundedly reflexive in particular this assures that the commutant of any banach space operator is boundedly reflexive we also show that the bounded reflexive cover of the set of all toeplitz matrices in m m n is the entire m m n for finite dimensional banach spaces using kronecker canonical form for matrix pencils we obtain some necessary and sufficient conditions for the kernels to be boundedly reflexive these conditions enable us to easily determine bounded reflexivity by simply computing rank or nullity of matrices

some algebraic structure of the riordan group abstract in this paper we highlight some of the algebraic properties of the riordan group we present some new properties and provide proofs for some known properties for instance proofs of properties of the power bell and derivative subgroups are presented we also give a new property for generating stochastic riordan matrices which are elements of the stochastic riordan subgroup centralizers stabilizers and certain riordan group isomorphisms are also given and proved we conclude by proving some properties connecting similar riordan matrices and pseudo involutions in the riordan group

parametric catalan numbers and catalan triangles abstract here presented a generalization of catalan numbers and catalan triangles associated with two parameters based on the sequence characterization of bell type riordan arrays among the generalized catalan numbers a class of large generalized catalan numbers and a class of small generalized catalan numbers are defined which can be considered as an extension of large schroder numbers and small schroder numbers respectively using the characterization sequences of bell type riordan arrays some properties and expressions including the taylor expansions of generalized catalan numbers are given a few combinatorial interpretations of the generalized catalan numbers are also provided finally a generalized motzkin numbers and motzkin triangles are defined similarly an interrelationship among parametrical catalan triangle pascal triangle and motzkin triangle is presented based on the sequence characterization of bell type riordan arrays

algebraic reflexivity of isometry groups and automorphism groups of some operator structures abstract we establish the algebraic reflexivity of three isometry groups of operator structures the group of all surjective isometries on the unitary group the group of all surjective isometries on the set of all positive invertible operators equipped with the thompson metric and the group of all surjective isometries on the general linear group of b h the operator algebra over a complex infinite dimensional separable hilbert space h we show that those isometry groups coincide with certain groups of automorphisms of corresponding structures and hence we also obtain the reflexivity of some automorphism groups

nonintersecting paths pfaffians and plane partitions gessel and viennot have developed a powerful technique for enumerating various classes of plane partitions the purpose of this article is to show by similar means that one may use pfaffiants to enumerate configurations of nonintersecting paths in which the initial and or terminal vertices of the paths are allowed to vary over specified regions of the digraph this leads to the possibility of enumerating classes of plane partitions in which the shape is allowed to vary whereas the previous applications of gessel and viennot were largely confined to plane partitions of a given shape

riordan arrays and related polynomial sequences abstract in this paper we generalize the results due to luzon and moron and present a characterization of the generalized riordan arrays using this characterization we establish a recurrence for the generalized sheffer sequences and study some special types of polynomial sequences including the generalized lucas u sequence and v sequence and the generalized humbert polynomial sequence in particular by appealing to the factorizations of riordan arrays the umbral composition of polynomial sequences and the hadamard product of series we establish various relations among these polynomial sequences thus we give a unified approach to some well known polynomial sequences appeared in combinatorics and the theory of special functions

general preservers of invariant subspace lattices let b x be the space of all bounded linear operators on a banach space x and let lata be the lattice of invariant subspaces of the operator a b x we characterize some maps b x b x with one of the following preserving properties lat a b lat a b or lat a b lat ab or lat a b b a lat ab ba or lat a b a lat aba or lat a b lat a b

combinatorics of a generalized narayana identity abstract the narayana identity is a well known formula that expresses the classical catalan numbers as sums of the ordinary narayana numbers in this paper we generalize the narayana identity to a family of riordan arrays including the array of ballot numbers the classical catalan triangle and several generalized catalan triangles recently studied a combinatorial description based on non crossing partitions is given for this identity for the column recursive rule and for the sheffer sequence associated with any array of the family

local derivations and local automorphisms in this paper we show that if l is a completely distributive commutative subspace lattice or a j subspace lattice then the space of all bounded derivations of algl is reflexive we also study when local automorphisms on some algebras are automorphisms

q riordan representation abstract the aim of this study is to establish further theory of q riordan representation we emphasize that any q matrices can be obtained by q riordan representation then we analyse the structure of the entries in the matrix product of general q riordan matrices

maps which preserve norms of non symmetrical quotients between groups of exponentials of lipschitz functions let explip x1 explip x2 be a surjective mapping where x1x1 and x2x2 are compact metric spaces we prove that if satisfies the non symmetric quotient norm condition for the uniform norm gf 1 g f 1 f g explip x1 then is of the form f y 1 y f y if y k 1 y f y if y x2 k f explip x1 where x2 x1 x2 x1 is a homeomorphism and k is a closed open subset of x2x2 on the other hand if satisfies the non symmetric quotient norm condition for the lipschitz algebra norm gf 1 gf 1 l g f 1 g f 1 l f g explip x1 we show that is of the form f y 1 y f y y x2 f explip x1 or f y 1 y f y y x2 f explip x1 where x2 x1 x2 x1 is a surjective isometry

a note on reflexivity abstract we prove some new results on hadwin s general version of reflexivity that reduce the study of e reflexivity or e hyperreflexivity of a linear subspace to a smaller linear subspace by applying our abstract results we present a simple proof of d hadwin s theorem which states that every c algebra is approximately hyperreflexive we also prove that the image of any c algebra under any bounded unital homomorphism into the operators on a banach space is approximately reflexive we introduce a new version of reflexivity called approximate algebraic reflexivity and study its properties

riordan arrays associated with laurent series and generalized sheffer type groups a relationship between a pair of laurent series and riordan arrays is formulated in addition a type of generalized sheffer groups is defined by using riordan arrays with respect to power series with non zero coefficients the isomorphism between a generalized sheffer group and the group of the riordan arrays associated with laurent series is established furthermore appell associated bell and hitting time subgroups of the groups are defined and discussed a relationship between the generalized sheffer groups with respect to different type of power series is presented the equivalence of the defined riordan array pairs and generalized stirling number pairs is given a type of inverse relations of various series is constructed by using pairs of riordan arrays finally several applications involving various arrays polynomial sequences special formulas and identities are also presented as illustrative examples

isometries between function spaces surjective isometries between some classical function spaces are investigated we give a simple technical scheme which verifies whether any such isometry is given by a homeomorphism between corresponding hausdorff compact spaces in particular the answer is positive for the c x ac 0 1 lip0 x and lip0 x spaces provided with various natural norms

bijections and the riordan group one of the cornerstone ideas in mathematics is to take a problem and to look at it in a bigger space in this paper we examine combinatorial sequences in the context of the riordan group various subgroups of the riordan group each give us a different view of the original sequence in many cases this leads to both a combinatorial interpretation and to eco rewriting rules in this paper we will concentrate on just four of the subgroups of the riordan group to demonstrate some of the possibilities of this approach

structural properties of riordan matrices and extending the matrices abstract we consider an infinite lower triangular matrix l l n k n k n 0 and a sequence n n n 0 called the a b sequence such that every element l n 1 k 1 except lying in column 0 can be expressed as l n 1 k 1 i 0 n k m i l n ai k bi 0 0 where a and b are integers with a b m 0 and b 0 this concept generalizes the a sequence of a riordan matrix as a result we explore several structural properties of riordan matrices by means of a b sequences in particular if b

advanced determinant calculus a complement abstract this is a complement to my previous article advanced determinant calculus c krattenthaler advanced determinant calculus seminaire lotharingien combin 42 1999 the andrews festschrift article b42q 67 pp in the present article i share with the reader my experience of applying the methods described in the previous article in order to solve a particular problem from number theory g almkvist c krattenthaler j petersson some new formulas for experiment math 12 2003 441 456 moreover i add a list of determinant evaluations which i consider as interesting which have been found since the appearance of the previous article or which i failed to mention there including several conjectures and open problems

1 invariant sequences and truncated fibonacci sequences abstract let p i j i j 0 1 2 and d diag 1 0 1 1 1 2 as a linear transformation of the infinite dimensional real vector space r x0 x1 x2 t xi r for all i pd has only two eigenvalues 1 1 in this paper we find some matrices associated with p whose columns form bases for the eigenspaces for pd we also introduce truncated fibonacci sequences and truncated lucas sequences and show that these sequences span the eigenspaces of pd

hermitian operators on banach algebras of vector valued lipschitz maps abstract we study hermitian operators on an algebra of lipschitz maps with values in a uniform algebra as an application we present a characterization of a unital surjective isometry on a banach algebra of lipschitz maps with values in a unital c algebra

kadison singer algebras hyperfinite case a new class of operator algebras kadison singer algebras ks algebras is introduced these highly noncommutative non self adjoint algebras generalize triangular matrix algebras they are determined by certain minimally generating lattices of projections in the von neumann algebras corresponding to the commutant of the diagonals of the ks algebras a new invariant for the lattices is introduced to classify these algebras

riordan matrices in the reciprocation of quadratic polynomials we iterate contractive one degree polynomials with coefficients in the ring k x of formal power series to calculate the reciprocal in k x of a quadratic polynomial doing this we meet the structure of riordan array we interpret certain changes of variable as a riordan array we finish the paper by using our techniques to find new ways to get known formulas for the sum of powers of natural numbers involving stirling and eulerian numbers

on the minimal rank in non reflexive operator spaces over finite fields let u and v be vector spaces over a field k and s be an n dimensional linear subspace of l u v the space s is called algebraically reflexive whenever it contains every linear map g u v such that for all x u there exists f s with g x f x a theorem of meshulam and semrl states that if s is not algebraically reflexive then it contains a non zero operator of rank at most 2n 2 provided that k has more than n 2 elements in the present article we prove that the provision on the cardinality of the underlying field is unnecessary to do so we demonstrate that the above result holds for all finite fields

range compatible homomorphisms on matrix spaces abstract let k be a commutative field and u and v be finite dimensional vector spaces over k let s be a linear subspace of the space l u v of all linear operators from u to v a map f s v is called range compatible when f s im s for all s s obvious examples of such maps are the evaluation maps s s x with x u in this article we classify all the range compatible group homomorphisms on s provided that codim l u v s 2 dim v 3 unless k has cardinality 2 and codim l u v s 2 dim v 3 under those assumptions it is shown that the linear range compatible maps are the evaluation maps and the above upper bound on the codimension of s is optimal for this result to hold as an application we obtain new sufficient conditions for the algebraic reflexivity of an operator space and with the above conditions on the codimension of s we give an explicit description of the range restricting and range preserving homomorphisms on s

reflexivity of the automorphism and isometry groups of the suspension of b h the aim of this paper is to show that the automorphism and isometry groups of the suspension of b h h being a separable infinite dimensional hilbert space are algebraically reflexive this means that every local automorphism respectively every local surjective isometry ofc0 r b h is an automorphism respectively a surjective isometry

local lie derivations of nest algebras abstract let n be a nest on a hilbert space h and alg n be the associated nest algebra we prove that every local lie derivation from alg n into b h is a lie derivation

quantum theory the church turing principle and the universal quantum computer it is argued that underlying the church turing hypothesis there is an implicit physical assertion here this assertion is presented explicitly as a physical principle every finitely realizable physical system can be perfectly simulated by a universal model computing machine operating by finite means classical physics and the universal turing machine because the former is continuous and the latter discrete do not obey the principle at least in the strong form above a class of model computing machines that is the quantum generalization of the class of turing machines is described and it is shown that quantum theory and the universal quantum computer are compatible with the principle computing machines resembling the universal quantum computer could in principle be built and would have many remarkable properties not reproducible by any turing machine these do not include the computation of non recursive functions but they do include quantum parallelism a method by which certain probabilistic tasks can be performed faster by a universal quantum computer than by any classical restriction of it the intuitive explanation of these properties places an intolerable strain on all interpretations of quantum theory other than everett s some of the numerous connections between the quantum theory of computation and the rest of physics are explored quantum complexity theory allows a physically more reasonable definition of the complexity or knowledge in a physical system than does classical complexity theory

reflexivity algebraic reflexivity and linear interpolation introduction this paper was motivated by a discovery that most finite dimensional subalgebras of b h for h an infinite dimensional hilbert space are reflexive with the only obstructions to reflexivity being finite rank considerations proofs section 2 do not depend on multiplicative structure nor on topology so extend to linear subspaces of transformations in an abstract setting abstract reflexivity has been studied in 3 4 7 primarily for singly generated algebras reflexivity properties can be interpreted as linear interpolation properties and we shall adopt this point of view the results of section 2 extend in section 3 to algebraic reflexivity counterparts for countably generated algebraically linear subspaces of bounded linear transformations acting on a banach space as consequences in section 4 we obtain generalizations of two single operator results one is a multivariate version of the result due to kaplansky 10 theorem 15 that a bounded locally algebraic operator acting on a banach space is algebraic the other is a multivariate version of the result due to douglas and foias 5 for hilbert space and to hadwin 7 for a general banach space extending work of fillmore 6 that a bounded non algebraic operator acting on a banach space is topologically algebraically reflexive in section 5 we give an application kindly suggested by d hadwin concerning joint strong similarity orbits of n tupules of operators we wish to thank e azoff k davidson j erdos d hadwin j kraus c lance and a sourour for conversations and some correspon

reflexivity and hyperreflexivity of operator spaces abstract in this paper we show that if s is an n dimensional subspace of l v such that every nonzero transformation of s has rank greater than or equal to 2 n 1 then s is algebraically reflexive if s is an n dimensional subspace of b h such that every nonzero transformation of s has rank greater than or equal to 2 n 1 then s is hyperreflexive we also consider how to construct some new hyperreflexive subspaces