embedding c algebra extensions into af algebras abstract sufficient conditions are given for a c algebra extension to be embeddable into an af algebra when it is known that the ideal and quotient algebras can be so embedded an appliction is made to a class of type i c algebras

homotopy of unitaries in simple c algebras with tracial rank one let 0 be a positive number is there a number 0 satisfying the following given any pair of unitaries u and v in a unital simple c algebra a with v 0 in k1 a for which uv vu there is a continuous path of unitaries v t t 0 1 a such that v 0 v v 1 1and uv t v t u for allt 0 1 an answer is given to this question when a is assumed to be a unital simple c algebra with tracial rank no more than one let c be a unital separable amenable simple c algebra with tracial rank no more than one which also satisfies the uct suppose that c a is a unital monomorphism and suppose that v a is a unitary with v 0 in k1 a such that v almost commutes with it is shown that there is a continuous path of unitaries v t t 0 1 in a with v 0 v and v 1 1 such that the entire path v t almost commutes with provided that an induced bott map vanishes other versions of the so called basic homotopy lemma are also presented

crossed products of nuclear c algebras and their traces abstract this work addresses the blackadar kirchberg question bkq as it pertains to group and reduced crossed product c algebras the bkq asks if every stably finite c algebra admits the matricial field mf property we characterize the mf property for a class of reduced crossed product c algebras and for their traces we prove that every ordered abelian group is in a sense mf and show that there is no k theoretic obstruction to an affirmative answer to the bkq using classification techniques and induced k theoretic dynamics we give an affirmative answer to the bkq for reduced crossed products of ah algebras of real rank zero by free groups combining our results with recent progress in elliott s classification program shows that the reduced crossed product of a separable simple unital nuclear uct and monotracial c algebra by the free group is always mf we also examine traces on these crossed products and show they always admit certain finite dimensional approximation properties by appealing to a result of ozawa rordam and sato we show that semidirect products of discrete amenable groups by free groups admit mf reduced group c algebras

choquet type l 1 spaces of a vector capacity abstract given a set function with values in a banach space x we construct an integration theory for scalar functions with respect to by using duality on x and choquet scalar integrals our construction extends the classical bartle dunford schwartz integration for vector measures since just the minimal necessary conditions on are required several l 1 spaces of integrable functions associated to appear in such a way that the integration map can be defined in them we study the properties of these spaces and how they are related we show that the behavior of the l 1 spaces and the integration map can be improved in the case when x is an order continuous banach lattice providing new tools for non linear operator theory and information sciences

monotone measures and universal integrals in a uniform framework for the scientific impact assessment problem the choquet sugeno and shilkret integrals with respect to monotone measures as well as their generalization the universal integral stand for a useful tool in decision support systems in this paper we propose a general construction method for aggregation operators that may be used in assessing output of scientists we show that the most often currently used indices of bibliometric impact like hirsch s h woeginger s w egghe s g kosmulski s maxprod and similar constructions may be obtained by means of our framework moreover the model easily leads to some new very interesting functions

diffusions for global optimizations we seek a global minimum of u 0 1 n to r the solution to d dt x t nabla u x t will find local minima the solution to dx t nabla u x t dt sqrt 2t dw t where w is standard n dimensional brownian motion and the boundaries are reflecting will concentrate near the global minima of u at least when temperature t is small the equilibrium distribution for x t is gibbs with density pi t x alpha exp u x t this suggests setting t t t downarrow 0 to find the global minima of u we give conditions on u x and t t such that the solution to dx t nabla u x t dt sqrt 2t dw t converges weakly to a distribution concentrated on the global minima of u

the choquet integral in riesz space a comprehensive discussion of the theory of choquet integration in a riesz space is given in particular it is proved that the monotone convergence theorem the fatou lemma and the dominated convergence theorem are still valid for riesz space valued non additive measures if we assume that the riesz space has a new property concerning the cardinality of the set of points of discontinuity of a monotone function

mf actions and k theoretic dynamics we study the interplay of c dynamics and k theory notions of chain recurrence for transformations groups x and mf actions for non commutative c dynamical systems a are translated into k theoretical language where purely algebraic conditions are shown to be necessary and sufficient for a reduced crossed product to admit norm microstates we are particularly interested in actions of free groups on af algebras in which case we prove that a k theoretic coboundary condition determines whether or not the reduced crossed product is a matricial field mf algebra one upshot is the equivalence of stable finiteness and being mf for these reduced crossed product algebras

on lusin s theorem for non additive measures that take values in an ordered topological vector space abstract lusin s theorem was established for real valued monotone measures under an equivalent condition to egoroff s theorem recently in this paper we show that the same result remains valid for non additive measures that take values in an ordered topological vector space we apply our result to several ordered topological vector spaces

when is the cuntz krieger algebra of a higher rank graph approximately finite dimensional evans d g and sims a when is the cuntz krieger algebra of a higher rank graph approximately finite dimensional preprint arxiv 1112 4549v1

cuntz pimsner algebras crossed products and k theory abstract suppose a is a c algebra and h is a c correspondence over a if h is regular in the sense that the left action of a is faithful and is given by compact operators then we compute the k theory of o a h t where the action is the usual gauge action the case where a is an af algebra is carefully analyzed in particular if a is af we show o a h t is af combining this with takai duality and an af embedding theorem of n brown we show the conditions af embeddability quasidiagonality and stable finiteness are equivalent for o a h if h is also assumed to be regular these finiteness conditions can be characterized in terms of the ordered k theory of a

invariants of almost commuting unitaries abstract two invariants of pairs of almost commuting unitary matrices have been defined and used to identify those pairs which are bounded away from commuting pairs the first denoted k u v for unitaries u v mn c involved k theory while the second was defined via winding numbers we show that these invariants coincide we also establish some upper bounds on k u v

ordered k groups associated to substitutional dynamics the matsumoto k0 group is an interesting invariant of flow equivalence for symbolic dynamical systems because of its origin as the k theory of a certain c algebra which is also a flow invariant this group comes equipped with a flow invariant order structure we emphasize this order structure and demonstrate how methods from operator algebra and symbolic dynamics combine to allow a computation of it in certain cases including sturmian and primitive substitutional shifts in the latter case we show by example that the ordered group is a strictly finer invariant than the group itself

the ext class of an approximately inner automorphism let a be a simple unital at algebra of real rank zero it is shown below that the range of the natural map from the approximately inner automorphism group to kk a a coincides with the kernel of the map kk a a l 1 0 hom ki a ki a 1 introduction and preliminaries 1 1 an automorphism of a unital c algebra a is said to be an approximately inner automorphism if there is a sequence of unitaries un 2 a such that a limadun a for all a 2 a it follows that the induced map on k a is the identity map there is however an invariant of k theoretical interest which can occur nontrivial extensions may arise in the six term periodic sequence for the k theory of the mapping torus we show below that every extension does arise if a is a simple unital at algebra of real rank zero as an immediate corollary we obtain a stronger form of elliott s classification theorem for such algebras an invertible kk element that preserves positivity and the class of the unit lifts to an isomorphism 1 2 recall that a unital c algebra a is said to be a unital at algebra if it is expressible as the inductive limit of finite direct sums of algebras of the form mn c t with unital embeddings let a be a unital at algebra and let be an approximately inner automorphism of a the mapping torus of is the c algebra

non monotonic fuzzy measures and the choquet integral abstract this paper discusses non monotonic fuzzy measures which are set functions without monotonicity and the choquet integral with respect to non monotonic fuzzy measures a concrete example shows that the choquet integral is meaningful in the case of non monotonic fuzzy measures as well as in the case of ordinary fuzzy measures every comonotonically additive positively homogeneous functional of bounded variation can be represented as a choquet integral with respect to a non monotonic fuzzy measure of bounded variation the space of such functionals is a real banach space isometrically isomorphic to the space of non monotonic fuzzy measures of bounded variation

citation based journal ranks the use of fuzzy measures this article considers a real world application of the choquet integral based classifier to the problem of ranking of scientific journals we attempted to predict rankings given by panels of experts by using available citation indices we compare the choquet integral fit by the least absolute deviation criterion as a classifier against other ordinal classification methods before interpreting the fuzzy measure weights and indices our findings show that the journal rankings data set is difficult to model accurately due to inconsistencies and lack of monotonicity but that the choquet integral still performs well as a classifier

the rohlin property for shifts on uhf algebras and automorphisms of cuntz algebras abstract we show that the shift on the uhf algebra m n has the rohlin property for any odd n hence by brotteli et al the crossed product of a uhf algebra by a shift ergodic theory dynam systems 13 1993 615 626 for any n 2 3 and that any automorphism of the cuntz algebra o n n m is outer for any m 0

af embeddability of crossed products of af algebras by the integers ifais an af algebra and aut a it is shown that af embeddability of the crossed product a z is equivalent toa z being stably finite this equivalence follows from a simple k theoretic characterization of af embeddability it is then shown that ifa z is af embeddable then the af embedding can be chosen in such a way as to induce a rationally injective map onk0 a z

non commutative shifts and crossed products abstract when a is a unital simple af c algebra and has a unique tracial state it is shown that the crossed product of the two sided infinite tensor product z a by the shift is a tracially af c algebra a similar result is given to the crossed product of a certain non unital two sided infinite tensor product by the shift applying a far reaching classification result of such c algebras by h lin we obtain an example of a one parameter automorphism group on some af c algebra which is not approximately inner a counter example to the af version of the so called powers sakai conjecture 23

the h index and the number of citations two fuzzy integrals in this paper we review two of the most well known citation indexes and establish their connections with the choquet and sugeno integrals in particular we show that the recently established h index is a particular case of the sugeno integral and that the number of citations corresponds to the choquet integral in both cases they use the same fuzzy measure the results presented here permit one to envision new indexes defined in terms of fuzzy integrals using other types of fuzzy measures a few considerations in this respect are also included in this paper indexes for taking into account recent research and the publisher credibility are outlined

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

on sufficient conditions for the egoroff theorem of an ordered topological vector space valued non additive measure in this paper we consider an ordered vector space endowed with a locally full topology which is called an ordered topological vector space we show that the egoroff theorem remains valid for the ordered topological vector space valued non additive measure in the following four cases the first case is that the measure is strongly order totally continuous the second case is that the measure is strongly order continuous and possesses an additional continuity property suggested by sun in 1994 when the ordered topological vector space has a certain property the third case is that the measure is continuous from above and below when the topology is locally convex the fourth case is that the measure is uniformly autocontinuous from above continuous from below and strongly order continuous when the topology is locally convex our results are applicable to several ordered topological vector spaces

rotation entropy and equilibrium states for a dynamical system x t and function f x rd we consider the corresponding generalised rotation set this is the convex subset of rd consisting of all integrals of f with respect to t invariant probability measures we study the entropy h e of rotation vectors e and relate this to the directional entropy lhl l of geller misiurewicz for x t a mixing subshift of finite type and f of summable variation we prove that if the rotation set is strictly convex then the functions h and h are in fact one and the same for those rotation sets which are not strictly convex we prove that 1h e and h e can differ only at non exposed boundary points e

diffusion for global optimization in r n we seek a global minimum of u mathbb r n to mathbb r the solution to d dt x t nabla u x t will find local minima using the idea of simulated annealing we consider th

classification of certain infinite simple c algebras the class of c algebras that arise as the crossed product of a stable simple af algebra with a z action determined by an automorphism which maps a projection in the algebra onto a proper subprojection is proved to consist of simple purely infinite c algebras and a specific subclass of it is proved to be classified by k theory this subclass is large enough to exhaust all possible k groups if g0 and g1 are countable abelian groups with g1 torsion free as it must be then there is a c algebras a in the classified subclass with k0 a g0 and k 1 a g1 the subclass contains the cuntz algebras o with n even and the cuntz krieger algebras o a with k0 o a of finite old order and it is closed under forming inductive limits the c algebras in the classified subclass can be viewed as classifiable models in a strong sense of general simple purely infinite c algebras with the same k theory

c algebras of real rank zero abstract the concept of real rank of a c algebra is introduced as a non commutative analogue of dimension it is shown that real rank zero is equivalent to the previously defined conditions fs and hp and that it is invariant under strong morita equivalence in particular under stable isomorphism real rank zero is also invariant under inductive limits and split extensions and the class may well be regarded as the conceptual completion of the af algebras in some cases notably when the algebra is matroid it is shown that the multiplier algebra also has real rank zero although that is not true in general by a result of g j murphy this implies a weyl von neumann type result for self adjoint multiplier elements in these cases

homotopy of a pair of approximately commuting unitaries in a simple c algebra abstract it is shown that for a class of unital c algebras including purely infinite simple c algebras real rank zero simple a t algebras and af algebras ifuandvare almost commuting unitaries whereuhas trivialk1 class vhas full spectrum and a certaink0 valued obstruction associated to the pairu vis trivial thenucan be deformed to 1 through a path of unitaries in the algebra almost commuting withv and the length of the path can be estimated by a universal constant this result is used to identify the obstruction with loring s bott element associated to the pairu vand also to prove the more universal statement that if ui vi i 1 2 are two pairs of almost commuting unitaries with ui 1 vi 1 and bott ui vi each independent ofi then one pair can be deformed into the other along a path of pairs of almost commuting unitaries in the algebra the length of the path being bounded by a universal constant

constrained restoration and the recovery of discontinuities the linear image restoration problem is to recover an original brightness distribution x sup 0 given the blurred and noisy observations y kx sup 0 b where k and b represent the point spread function and measurement error respectively this problem is typical of ill conditioned inverse problems that frequently arise in low level computer vision a conventional method to stabilize the problem is to introduce a priori constraints on x sup 0 and design a cost functional h x over images x which is a weighted average of the prior constraints regularization term and posterior constraints data term the reconstruction is then the image x which minimizes h a prominent weakness in this approach especially with quadratic type stabilizers is the difficulty in recovering discontinuities the authors therefore examine prior smoothness constraints of a different form which permit the recovery of discontinuities without introducing auxiliary variables for marking the location of jumps and suspending the constraints in their vicinity in this sense discontinuities are addressed implicitly rather than explicitly

stability for integer actions on uhf c algebras on montre qu il est possibile d obtenir une version norme continue de la solution de connes a la 1 cohomologie qui est adaptable a la situation des c algebres on exhibe diverses actions modeles stables

asymptotically unitary equivalence and asymptotically inner automorphisms let c be a unital ah algebra and let a be a unital separable simple c algebra with tracial rank zero suppose that phi 1 phi 2 colon c to a are two unital monomorphisms we show that there is a continuous path of unitaries u t colon t in 0 infty of a such that lim t to infty u t phi 1 a u t phi 2 a quad hbox rm for all quad a in c if and only if phi 1 phi 2 in kk c a tau circ phi 1 tau circ phi 2 for all tau in t a and the rotation map tilde eta phi 1 phi 2 associated with phi 1 and phi 2 is zero in particular an automorphism alpha on a unital separable simple c algebra a in cal n with tracial rank zero is asymptotically inner if and only if alpha rm id a quad rm in quad kk a a and the rotation map tilde eta phi 1 phi 2 is zero let a be a unital ah algebra not necessarily simple and let alpha in aut a be an automorphism as an application we show that the associated crossed product a rtimes alpha bbb z can be embedded into a unital simple af algebra if and only if a admits a strictly positive alpha invariant tracial state

toeplitz minimal flows which are not uniquely ergodic we study minimal symbolic dynamical systems which are orbit closures of toeplitz sequences we construct 0 1 subshifts of this type for which the set of ergodic invariant measures has any given finite cardinality is countably infinite or has cardinality of the continuum

mathbb z actions on ah algebras and mathbb z 2 actions on af algebras we consider mathbb z actions single automorphisms on a unital simple ah algebra with real rank zero and slow dimension growth and show that the uniform outerness implies the rohlin property under some technical assumptions moreover two mathbb z actions with the rohlin property on such a c algebra are shown to be cocycle conjugate if they are asymptotically unitarily equivalent we also prove that locally approximately inner and uniformly outer mathbb z 2 actions on a unital simple af algebra with a unique trace have the rohlin property and classify them up to cocycle conjugacy employing the orderext group as classification invariants

af embeddability of crossed products of at algebras by the integers and its application abstract we will show that the crossed products of unital simple real rank zero at algebras by the integers are af embeddable this is a generalization of brown s af embedding theorem as an application we will prove the af embeddability of crossed product algebras arising from certain minimal dynamical systems induced by two commuting homeomorphisms

vector valued information measures and integration with respect to fuzzy vector capacities abstract integration with respect to vector valued fuzzy measures is used to define and study information measuring tools motivated by some current developments in information science we apply the integration of scalar functions with respect to vector valued fuzzy measures also called vector capacities bartle dunford schwartz integration for the additive case and choquet type integration for the non additive case are considered showing that these formalisms can be used to define and develop vector valued impact measures examples related to existing bibliometric tools as well as to new measuring indices are given

unbounded derivations in at algebras letabe a simple unital at algebra of real rank zero such that it has a unique tracial state andk1 a is neither 0 norz for each hom k1 a r with dense range inrwe construct a closed derivation inawhich generates a one parameter automorphism group ofasuch that u u 2 i u for any unitaryu d furthermore we construct such an with the rohlin property which is defined in kishimoto comm math phys 179 1996 599 622 in this case the crossed producta ris a simple at algebra of real rank zero as an application we obtain that for such ac algebraathe kernel of the natural homomorphism of the groupinn a of approximately inner automorphisms intoext k1 a k0 a ext k0 a k1 a is the group hinn a of automorphisms homotopic to inner automorphisms combining with the result of kishimoto and kumjian trans amer math soc to appear inn a hinn a is isomorphic to the above direct sum as another application of the construction of derivations we show that ifais ac algebra of the above type and hinn a has the rohlin property and comes from hom k1 a r with dense range as in kishimoto and kumjian preprint then the crossed producta zis again of the same type in particulara zis an at algebra the other properties are known from kishimoto j operator theory40 1998

exact number of ergodic invariant measures for bratteli diagrams abstract for a bratteli diagram b we study the simplex m 1 b of probability measures on the path space of b which are invariant with respect to the tail equivalence relation equivalently m 1 b is formed by probability measures invariant with respect to a homeomorphism of a cantor set we study relations between the number of ergodic measures from m 1 b and the structure and properties of the diagram b we prove a criterion and find sufficient conditions of unique ergodicity of a bratteli diagram in which case the simplex m 1 b is a singleton for a finite rank k bratteli diagram b having exactly l k ergodic invariant measures we explicitly describe the structure of the diagram and find the subdiagrams which support these measures we find sufficient conditions under which i a bratteli diagram has a prescribed number finite or infinite of ergodic invariant measures and ii the extension of a measure from a uniquely ergodic subdiagram gives a finite ergodic invariant measure several examples including stationary bratteli diagrams pascal bratteli diagrams and toeplitz flows are considered

a universal integral as common frame for choquet and sugeno integral the choquet and the sugeno integral provide a useful tool in many problems in engineering and social choice where the aggregation of data is required however their applicability is restricted because of the special operations used in the construction of these integrals therefore we provide a concept of integrals generalizing both the choquet and the sugeno case for functions with values in the nonnegative real numbers universal integrals are introduced and investigated which can be defined on arbitrary measurable spaces and for arbitrary monotone measures for a fixed pseudo multiplication on the nonnegative real numbers the smallest and the greatest universal integrals are given finally another construction method for obtaining universal integrals is introduced and the restriction to the unit interval i e to fuzzy integrals is considered

pseudo lp space and convergence in the framework of the pseudo analysis the classical l p space is generalized and there are proved important properties of introduced space three types of convergence of sequences of measurable functions are considered in this space the inequalities for integrals based on pseudo integral have been recently proposed as the holder minkowski and markov inequalities which are applied in observing relationship among introduced convergences

rotation sets and almost periodic sequences we study the rotational behaviour on minimal sets of torus homeomorphisms and show that the associated rotation sets can be any type of line segment as well as non convex and even plane separating continua this shows that the restriction which hold for rotation sets on the whole torus are not valid on minimal sets the proof uses a construction of rotational horseshoes by kwapisz to transfer the problem to a symbolic level where the desired rotational behaviour is implemented by means of suitable irregular toeplitz sequences

crossed products of the cantor set by free minimal actions of ℤd let d be a positive integer let x be the cantor set and let d act freely and minimally on x we prove that the crossed product c d x has stable rank one real rank zero and cancellation of projections and that the order on k0 c d x is determined by traces we obtain the same conclusion for the c algebras of various kinds of aperiodic tilings

a rohlin property for one parameter automorphism groups we define a rohlin property for one parameter automorphism groups of unital simplec algebras and show that for such an automorphism group any cocycle is almost a coboundary we apply the same method to the single automorphism case and show that if an automorphism of a unital simplec algebra with a certain condition has a central sequence of approximate eigen unitaries for any complex number of modulus one then any cocycle is almost a coboundary or the automorphism has the stability we also show that if a one parameter automorphism group of a unital separable purely infinite simplec algebra has the rohlin property then the crossed product is simple and purely infinite

global optimization by adapted diffusion in this paper we study a diffusion stochastic dynamics with a general diffusion coefficient the main result is that adapting the diffusion coefficient to the hamiltonian allows to escape local wide minima and to speed up the convergence of the dynamics to the global minima we prove the convergence of the invariant measure of the modified dynamics to a measure concentrated on the set of global minima and show how to choose a diffusion coefficient for a certain class of hamiltonians

an approximate universal coefficient theorem an approximate universal coefficient theorem auct for certain c algebras is established we present a proof that kirchberg phillips s classification theorem for separable nuclear purely infinite simple c algebras is valid for c algebras satisfying the auct instead of the uct it is proved that two versions of auct are in fact the same we also show that c algebras that are locally approximated by c algebras satisfying the auct satisfy the auct as an application we prove that certain simple c algebras which are locally type i are in fact isomorphic to simple ah algebras as another application we show that a sequence of residually finite dimensional c algebras which are asymptotically nuclear and which asymptotically satisfies the auct can be embedded into the same simple af algebra

af embeddability of crossed products of cuntz algebras abstract we investigate crossed products of cuntz algebras by quasi free actions of abelian groups we prove that our algebras are af embeddable when actions satisfy a certain condition we also give a necessary and sufficient condition that our algebras become simple and purely infinite and consequently our algebras are either purely infinite or af embeddable when they are simple

af embeddability of 2 graph algebras and quasidiagonality of k graph algebras abstract we characterise quasidiagonality of the c algebra of a cofinal k graph in terms of an algebraic condition involving the coordinate matrices of the graph this result covers all simple k graph c algebras in the special case of cofinal 2 graphs we further prove that af embeddability quasidiagonality and stable finiteness of the 2 graph algebra are all equivalent