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

crossed products by endomorphisms of c_0 x algebras abstract in the first part of the paper we develop a theory of crossed products of a c algebra a by an arbitrary not necessarily extendible endomorphism a a we consider relative crossed products c a j where j is an ideal in a and describe up to morita rieffel equivalence all gauge invariant ideals in c a j and give six term exact sequences determining their k theory we also obtain certain criteria implying that all ideals in c a j are gauge invariant and that c a j is purely infinite in the second part we consider a situation where a is a c 0 x algebra and is such that f a f a a a f c 0 x where is an endomorphism of c 0 x pictorially speaking is a mixture of a topological dynamical system x dual to c 0 x and a continuous field of homomorphisms x between the fibers a x x x of the corresponding c bundle for systems described above we establish efficient conditions for the uniqueness property gauge invariance of all ideals and pure infiniteness of c a j we apply these results to the case when x prim a is a hausdorff space in particular if the associated c bundle is trivial we obtain formulas for k groups of all ideals in c a j in this way we constitute a large class of crossed products whose ideal structure and k theory is completely described in terms of x x x x y where y is a closed subset of x

generalizations of the fkkm theorem and the ky fan minimax inequality with applications to maximal elements price equilibrium and complementarity abstract this paper generalizes the fan knaster kuratowski mazurkiewicz fkkm theorem of ky fan game theory and related topics pp 151 156 north holland amsterdam 1979 and math ann 266 1984 519 537 and the ky fan minimax inequality by introducing a class of the generalized closedness and continuity conditions which are called the transfer closedness and transfer continuities we then apply these results to prove the existence of maximal elements of binary relations under very weak assumptions we also prove the existence of price equilibrium and the complementarity problem without the continuity assumptions thus our results generalize many of the existence theorems in the literature

approximation and fixed point theorems for condensing composites of multifunctions one of the authors previously extended an interesting best approximation theorey of ky fan to condensing maps defined on a closed ball in a banach space and defined on a closed convex subset in a hilbert space recently there have appeared a number of new results on fixed points of so called kakutani factorizable multifunctions or composites of acyclic or other type of multifunctions defined on convex subsets of topological vector spaces in this paper we extend lin s results to the multifunction or set valued version for the above mentioned factorizable multifunctions applications to fixed point theorems are given

moment method analysis of large axially symmetric reflector antennas using entire domain functions the moment method technique utilizing entire domain basis functions is applied to the analysis of large axially symmetric reflector antennas the electric surface current is modeled as a finite series of sinusoids whose domain consists of the entire generating curve this expansion results in a matrix size of less than 5 of that produced with subdomain basis functions only a slight increase in the cpu requirements occurs from this analysis the results from this technique show good agreement when compared to both physical optics and a subdomain based moment method formulation on small axially fed paraboloidal and hyperboloidal reflector antennas extension to a large 100 lambda paraboloidal reflector with f d 0 4 produces results comparable to that obtained using physical optics convergence is obtained with as few as two expansion terms per wavelength discretization of the generating curve with four points per wavelength leads to results which agree within 0 5 db over data from a more densely defined curve

using half plane solutions in the context of mm for analyzing large flat structures with or without resistive loadings the size of the scatterers that can be analyzed using the conventional method of moments mm is limited to only a few wavelengths due to large storage requirements in the computer one way to circumvent this problem is to use techniques that temper the growth in the size of the impedance matrix to a reasonable level even as the scatterer becomes large in terms of the wavelength it is shown that this can be done by choosing an appropriate set of entire or semi entire domain basis functions that incorporate the actual physics of the scattering phenomenon the functional forms of the basis functions are obtained either from an exact or an asymptotic solution to certain canonical problems as an example the problems of scattering from perfectly conducting or resistively loaded flat strips and plates are solved by utilizing the exact or asymptotic solutions to half plane problems as basis functions

purely infinite partial crossed products let a g be a partial dynamical system we show that there is a bijective correspondence between g invariant ideals of a and ideals in the partial crossed product a rg provided the action is exact and residually topologically free assuming in addition a technical condition automatic when a is abelian we show that a rg is purely infinite if and only if the positive nonzero elements in a are properly infinite in a rg as an application we verify pure infiniteness of various partial crossed products including realisations of the cuntz algebras on oa on and oz as partial crossed products

the use of curved segments for numerically modeling thin wire antennas and scatterers to reduce the number of segments required to model curved wire structures a method of moments formulation using curved wire segments is presented piecewise quadratic wire segments are used to discretize the wire geometry this algorithm is used to analyze a small wire loop antenna and multiple arm archimedian spiral antenna for each example a comparison is made between results obtained using this quadratic segment algorithm and a linear segment algorithm these examples demonstrate that the memory required is significantly reduced and a reduction in the solution time is achieved when quadratic segments are used

fixed point theorems for compact multimaps on almost γ convex sets in generalized convex spaces abstract in this paper we introduce the concept of the strict kakutani multimap kkm property and investigate the fixed point problem for multimaps having this property on almost convex subsets of locally g convex uniform spaces our new fixed point theorem generalizes the well known fan glicksberg fixed point theorem and partially extends the himmelberg fixed point theorem its application to minimax theorem is also given

electromagnetic scattering from extended wires and two and three dimensional surfaces efficient numerical solutions for the electromagnetic scattering for classes of electrically large one two and three dimensional perfectly conducting scatterers are presented the formulation is based on solution of the electric field integral equation efie using the method of moments mm an entire domain galerkin representation is used for wires and two dimensional surfaces and a combination of entire and subdomain representations is applied to surfaces in three dimensions the analysis is extendable to corrugated surfaces formed from sections of surfaces of translation or rotation numerical results are presented for wires infinite strips and finite strips or plates the behavior of the solutions with the number of terms in the entire domain expansion is examined the reconstruction of the traveling wave contribution to the scattering cross section using various approximations is discussed and representative examples are given

an intersection theorem with applications in minimax theory and equilibrium problem in this paper we obtain a very general intersection theorem for the values of a map from this we derive an analytic alternative a new type of minimax inequality and an alternative theorem concerning three abstract equilibrium problems

non simple purely infinite c algebras the hausdorff case abstract local and global definitions of pure infiniteness for a c algebra a are compared and equivalence between them is obtained if the primitive ideal space of a is hausdorff and of finite dimension if a has real rank zero or if a is approximately divisible sufficient criteria are given for local pure infiniteness of tensor products they yield that exact simple tensorially non prime c algebras are purely infinite if they have no semi finite lower semi continuous trace one obtains that a is isomorphic to a o if a is 1 purely infinite separable stable nuclear and prim a is a hausdorff space not necessarily of finite dimension

electromagnetic scattering from electrically large coated flat and curved strips entire domain galerkin formulation efficient numerical solutions are presented for electromagnetic scattering for classes of electrically large coated perfectly conducting strips which are flat or curved the formulation is based on the solution of a coupled system of electric and magnetic field integral equations using the method of moments mm entire domain galerkin representations for the currents are used on the surface of the coating and at the coating conductor interface the resulting symmetric matrix equation is well conditioned and admits rapid accurate solutions numerical results are presented for various coating thicknesses strip widths and curvatures for the transverse electric te and transverse magnetic tm cases the convergence of the galerkin solution is examined as a function of these parameters the effect of the edge approximation on the choice of expansion functions is discussed the numerical results are compared with experimental measurements

fixed point theorems for multifunctions having kkm property on almost convex sets in this paper for two nonempty subsets x and y of a linear space e we define the class kkm x y and investigate the fixed point problem for t kkm x x with x an almost convex subset of a locally convex space our fixed point theorem contains lassonde fixed point theorem for kakutani factorizable multifunctions as special case

on general best proximity pairs and equilibrium pairs in free abstract economies abstract in this paper using lassonde s fixed point theorem for kakutani factorizable multifunctions and park s fixed point theorem for acyclic factorizable multifunctions we will prove new existence theorems for general best proximity pairs and equilibrium pairs for free abstract economies which generalize the previous best proximity theorems and equilibrium existence theorems due to srinivasan and veeramani p s srinivasan p veeramani on best approximation pair theorems and fixed point theorems abstr appl anal 2003 1 2003 33 47 p s srinivasan p veeramani on existence of equilibrium pair for constrained generalized games fixed point theory appl 2004 1 2004 21 29 and kim and lee w k kim k h lee existence of best proximity pairs and equilibrium pairs j math anal appl 316 2006 433 446 in several aspects

on mixed variational relation problems in this paper we exploit the method of variational relations to establish existence of solutions to a general inclusion problem the result is applied to variational relation problems in which several relations are simultaneously considered particular cases of variational inclusion and intersection of set valued maps are also discussed

existence of best proximity pairs and equilibrium pairs in this paper using the fixed point theorem for kakutani factorizable multifunctions we shall prove new existence theorems of best proximity pairs and equilibrium pairs for free abstract economies which include the previous fixed point theorems and equilibrium existence theorems

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

crossed products by endomorphisms and reduction of relations in relative cuntz pimsner algebras abstract starting from an arbitrary endomorphism of a unital c algebra a we construct a crossed product it is shown that the natural construction depends not only on the c dynamical system a but also on the choice of an ideal j orthogonal to ker the article gives an explicit description of the internal structure of this crossed product and in particular discusses the interrelation between relative cuntz pimsner algebras and partial isometric crossed products we present a canonical procedure that reduces any given c correspondence to the smallest c correspondence yielding the same relative cuntz pimsner algebra as the initial one in the context of crossed products this reduction procedure corresponds to the reduction of c dynamical systems and allows us to establish a coincidence between relative cuntz pimsner algebras and crossed products introduced

fixed points for kakutani factorizable multifunctions abstract a multifunction is called a kakutani multifunction if there exist two nonempty convex sets x and y each in a hausdorff topological vector space such that x y is upper semi continuous with nonempty compact convex values we prove the following extension of the kakutani fixed point theorem let x x be a multifunction from a simplex x into itself if can be factorized by an arbitrary finite number of kakutani multifunctions then has a fixed point the proof relies on a simplicial approximation technique and the brouwer fixed point theorem extensions to infinite dimensional spaces and applications to game theory are given

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

electromagnetic scattering from ducts with irregular edges ii noncircular case a formulation is developed for electromagnetic scattering from finite circular ducts terminated with irregular edges the analysis is based on the solution of the electric field integral equation using an entire domain galerkin expansion for both the axial and the circumferential variation of the currents defined in terms of an edge slope dependent vector field that provides simplifying symmetry properties for the method of moments system matrix comparisons are made with edge slope independent formulations the analysis is general and applicable for cases in which the functional variation of the edge irregularities is specified by either a deterministic or a random process circumferential modal decoupling occurs when the irregularities are specified by a stationary stochastic process having a periodic correlation function numerical results are given for edge irregularities governed by a gaussian random process and are compared for various limiting cases with results for right circular cylindrical ducts

purely infinite crossed products by endomorphisms 2013 elsevier inc all rights reserved this is the authors accepted and refereed manuscript to the article author s post print must be released with a creative commons attribution non commercial no derivatives license

pure infiniteness and ideal structure of c algebras associated to fell bundles abstract we investigate structural properties of the reduced cross sectional algebra c r b of a fell bundle b over a discrete group g conditions allowing one to determine the ideal structure of c r b are studied notions of aperiodicity paradoxicality and b infiniteness for the fell bundle b are introduced and investigated by themselves and in relation to the partial dynamical system dual to b several criteria of pure infiniteness of c r b are given it is shown that they generalize and unify corresponding results obtained in the context of crossed products by the following duos laca spielberg 34 jolissaint robertson 21 sierakowski rordam 47 giordano sierakowski 18 and ortega pardo 39 for exact separable fell bundles satisfying the residual intersection property primitive ideal space of c r b is determined the results of the paper are shown to be optimal when applied to graph c algebras applications to a class of exel larsen crossed products are presented

mathcal c _ 0 x algebras stability and strongly self absorbing mathcal c algebras we study permanence properties of the classes of stable and so called mathcal d stable mathcal c algebras respectively more precisely we show that a mathcal c 0 x algebra a is stable if all its fibres are provided that the underlying compact metrizable space x has finite covering dimension or that the cuntz semigroup of a is almost unperforated a condition which is automatically satisfied for mathcal c algebras absorbing the jiang su algebra mathcal z tensorially furthermore we prove that if mathcal d is a k 1 injective strongly self absorbing mathcal c algebra then a absorbs mathcal d tensorially if and only if all its fibres do again provided that x is finite dimensional this latter statement generalizes results of blanchard and kirchberg we also show that the condition on the dimension of x cannot be dropped along the way we obtain a useful characterization of when a mathcal c algebra with weakly unperforated cuntz semigroup is stable which allows us to show that stability passes to extensions of mathcal z absorbing mathcal c algebras

simple purely infinite c algebras and n filling actions let n be a positive integer we introduce a concept which we call the n filling property for an action of a group on a separable unital c algebra a if a c is a commutative unital c algebra and the action is induced by a group of homeomorphisms of then the n filling property reduces to a weak version of hyperbolicity the n filling property is used to prove that certain crossed product c algebras are purely infinite and simple a variety of group actions on boundaries of symmetric spaces and buildings have the n filling property an explicit example is the action of sln z on the projective n space

best proximity pairs and equilibrium pairs for kakutani multimaps new existence theorems of best proximity pairs for a finite family of kakutani multimaps are proved in a normed space setting as applications new existence theorems of equilibrium pairs for free n person and 1 person games are obtained our results generalize and improve several well known results 2008 elsevier ltd all rights reserved

compressibility a property of topological spaces related to abstract convexity abstract an abstract operation of hull in a set y associates with every finite set f y a set hull f y a topological space x is said to be compressible into a topological space y equipped with an operation of hull if for every sequence a1 an of open sets covering x and every y1 yn yn there exists a continuous function x y such that for every x x x hull y i x a i the concept of compressibility is extremely useful when dealing with problems of the existence of fixed points continuous selections or with kkm property the obtained results generalize several known theorems they also provide a broad range of new original results

fixed points coincidence points and maximal elements with applications to generalized equilibrium problems and minimax theory abstract in this paper using a generalization of the fan browder fixed point theorem we obtain a new fixed point theorem for multivalued maps in generalized convex spaces from which we derive several coincidence theorems and existence theorems for maximal elements applications of these results to generalized equilibrium problems and minimax theory will be given in the last sections of the paper

a c algebra of singular integral operators with shifts admitting distinct fixed points abstract representations on hilbert spaces for a nonlocal c algebra b of singular integral operators with piecewise slowly oscillating coefficients extended by a group of unitary shift operators are constructed the group of unitary shift operators u g in the c algebra b is associated with a discrete amenable group g of orientation preserving piecewise smooth homeomorphisms g t t that acts topologically freely on t and admits distinct fixed points for different shifts a c algebra isomorphism of the quotient c algebra b k where k is the ideal of compact operators onto a c algebra of fredholm symbols is constructed by applying the local trajectory method spectral measures and a lifting theorem as a result a fredholm symbol calculus for the c algebra b or equivalently a faithful representation of the quotient c algebra b k on a suitable hilbert space is constructed and a fredholm criterion for the operators b b is established

mixed domain galerkin expansions in scattering problems entire domain galerkin expansions provide a computationally efficient representation in method of moments mm solutions for electrically extended surfaces forming part of a separable coordinate geometry for surfaces not conforming to such geometries such as those with discontinuities subdomain representations have been used for many classes of scattering problems involving electrically large two dimensional scatterers with localized discontinuities a mixed domain galerkin expansion is shown to lead to a computationally efficient formulation electromagnetic scattering solutions are developed for such configurations convergence of these solutions is illustrated with choices of mixed domain expansions as a function of surface discontinuity the computed results are given for both transverse magnetic tm and transverse electric te polarization and are compared with published results

coincidence and maximal element theorems and their applications to generalized equilibrium problems and minimax inequalities abstract in this paper we obtain first a very general coincidence theorem from this we derive a new coincidence theorem and two alternative theorems concerning existence of maximal elements applications of these results to generalized equilibrium problems and minimax inequalities are given in the last sections

on c algebras associated with c correspondences abstract we study c algebras arising from c correspondences which were introduced by the author we prove the gauge invariant uniqueness theorem and obtain conditions for our c algebras to be nuclear exact or satisfy the universal coefficient theorem we also obtain a 6 term exact sequence of k groups involving the k groups of our c algebras

non simple purely infinite c algebras a c algebra a is defined to be purely infiniteif there are no characters on a a nd if for every pair of positive elements a b in a such that b lies in the closed two sided ideal generated by a there exists a sequence rn in a such that rn arn b this definition agrees with the usual definition by j cuntz when a is simple it is shown that the property of being purely infinite is preserved under extensions morita equivalence inductive limits and it passes to quotients and to hereditary sub c algebras it is shown that a is purely infinite for every c algebra a purely infinite c algebras admit no traces and conversely an approximately divisible exact c algebra is purely infinite if it admits no nonzero trace

crossed products by spectrally free actions abstract we define spectral freeness for actions of discrete groups on c algebras we relate spectral freeness to other freeness conditions an example result is that for an action of a finite group g spectral freeness is equivalent to strong pointwise outerness and also to the condition that g 1 for every g g 1 we then prove permanence results for reduced crossed products by exact spectrally free actions for crossed products by arbitrary actions of z 2 z and for extensions direct limits stable isomorphism and several related constructions for the following properties the combination of pure infiniteness and the ideal property residual hereditary infiniteness closely related to pure infiniteness residual sp a strengthening of property sp suitable for nonsimple c algebras the weak ideal property closely related to the ideal property for the weak ideal property we can allow arbitrary crossed products by any finite abelian group these properties of c algebras are shown to have formulations of the same general type allowing them all to be handled using a common set of theorems

scattering from wires and open circular cylinders of finite length using entire domain galerkin expansions electromagnetic em scattering by finite length perfectly conducting open cylinders i e ducts or tubes with circular cross sections is considered the case of a straight wire viewed as a thin cylinder is examined in this context the salient features of this study are a use of the electric field integral equation efie as a starting point b solution of this equation by the galerkin method and c representation of the axial variation of the currents on the scatterer by an entire domain fourier series expansion edge modes are considered in the expansion set and their effect is examined the open cylinder backscatter cross section is computed as a function of aspect angle for various radii and lengths and is compared with measured data

topological freeness for c correspondences abstract we study conditions that ensure uniqueness theorems of cuntz krieger type for relative cuntz pimsner algebras o j x associated to a c correspondence x over a c algebra a we give general sufficient conditions phrased in terms of a multivalued map x acting on the spectrum a of a when x j is of type i we construct a directed graph dual to x and prove a uniqueness theorem using this graph when x j is liminal we show that topological freeness of this graph is equivalent to the uniqueness property for o j x as well as to an algebraic condition which we call j acyclicity of x as an application we improve the fowler raeburn uniqueness theorem for the toeplitz algebra t x we give new simplicity criteria for o x we generalize and enhance uniqueness results for relative quiver c algebras of muhly and tomforde we also discuss applications to crossed products by endomorphisms