共查询到20条相似文献,搜索用时 15 毫秒
1.
The paper aims at developing a theory of nuclear (in the topological algebraic sense) pro-C*-algebras (which are inverse limits of C*-algebras) by investigating completely positive maps and tensor products. By using the structure of matrix algebras over a
pro-C*-algebra, it is shown that a unital continuous linear map between pro-C*-algebrasA andB is completely positive iff by restriction, it defines a completely positive map between the C*-algebrasb(A) andb(B) consisting of all bounded elements ofA andB. In the metrizable case,A andB are homeomorphically isomorphic iff they are matricially order isomorphic. The injective pro-C*-topology α and the projective pro-C*-topology v on A⊗B are shown to be minimal and maximal pro-C*-topologies; and α coincides with the topology of biequicontinous convergence iff eitherA orB is abelian. A nuclear pro-C*-algebraA is one that satisfies, for any pro-C*-algebra (or a C*-algebra)B, any of the equivalent requirements; (i) α =v onA ⊗B (ii)A is inverse limit of nuclear C*-algebras (iii) there is only one admissible pro-C*-topologyon A⊗B (iv) the bounded partb(A) ofA is a nuclear C⊗-algebra (v) any continuous complete state map A→B* can be approximated in simple weak* convergence by certain finite rank complete state maps. This is used to investigate permanence properties of nuclear pro-C*-algebras pertaining to subalgebras, quotients and projective and inductive limits. A nuclearity criterion for multiplier
algebras (in particular, the multiplier algebra of Pedersen ideal of a C*-algebra) is developed and the connection of this C*-algebraic nuclearity with Grothendieck’s linear topological nuclearity is examined. A σ-C*-algebraA is a nuclear space iff it is an inverse limit of finite dimensional C*-algebras; and if abelian, thenA is isomorphic to the algebra (pointwise operations) of all scalar sequences. 相似文献
2.
3.
Kazuyuki Sait 《Journal of Mathematical Analysis and Applications》2009,360(2):369-376
Akemann showed that any von Neumann algebra with a weak* separable dual space has a faithful normal representation on a separable Hilbert space. He posed the question: If a C*-algebra has a weak* separable state space, must it have a faithful representation on a separable Hilbert space? Wright solved this question negatively and showed that a unital C*-algebra has the weak* separable state space if and only if it has a unital completely positive map, into a type I factor on a separable Hilbert space, whose restriction to the self-adjoint part induces an order isomorphism. He called such a C*-algebra almost separably representable. We say that a unital C*-algebra is small if it has a unital complete isometry into a type I factor on a separable Hilbert space. In this paper we show that a unital C*-algebra is small if and only if the state spaces of all n by n matrix algebras over the C*-algebra are weak*-separable. It is natural to ask whether almost separably representable algebras are small or not. We settle this question positively for simple C*-algebras but the general question remains open. 相似文献
4.
The N-Isometric Isomorphisms in Linear N-Normed C^*-Algebras 总被引:3,自引:3,他引:0
Chun-Gil PARK Themistocles M. RASSIAS 《数学学报(英文版)》2006,22(6):1863-1890
We prove the Hyers-Ulam stability of linear N-isometries in linear N-normed Banach mod- ules over a unital C^*-algebra. The main purpose of this paper is to investigate N-isometric C^*-algebra isomorphisms between linear N-normed C^*-algebras, N-isometric Poisson C^*-algebra isomorphisms between linear N-normed Poisson C^*-algebras, N-isometric Lie C^*-algebra isomorphisms between linear N-normed Lie C^*-algebras, N-isometric Poisson JC^*-algebra isomorphisms between linear N-normed Poisson JC^*-algebras, and N-isometric Lie JC^*-algebra isomorphisms between linear N-normed Lie JC^*-algebras.
Moreover, we prove the Hyers- Ulam stability of t:heir N-isometric homomorphisms. 相似文献
5.
We will show that the bounded part of the locally C*-algebra of all adjointable operators on the Hilbert A-module E is isomorphic to the C*-algebra L
b(A)(b(E)) of all adjointable operators on the Hilbert b(A)-module b(E).
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
6.
We develop the method introduced previously, to construct infinitesimal generators on locally compact group C
*-algebras and on tensor product of C
*-algebras. It is shown in particular that there is a C
* -algebra A such that the C
*-tensor product of A and an arbitrary C
*-algebra B can have a non-approximately inner strongly one parameter group of *-automorphisms. 相似文献
7.
Karl-Hermann Neeb 《Semigroup Forum》2008,77(1):5-35
A host algebra of a topological group G is a C
*-algebra whose representations are in one-to-one correspondence with certain continuous unitary representations of G. In this paper we present an approach to host algebras for infinite dimensional Lie groups which is based on complex involutive
semigroups. Any locally bounded absolute value α on such a semigroup S leads in a natural way to a C
*-algebra C
*(S,α), and we describe a setting which permits us to conclude that this C
*-algebra is a host algebra for a Lie group G. We further explain how to attach to any such host algebra an invariant weak-*-closed convex set in the dual of the Lie algebra
of G enjoying certain nice convex geometric properties. If G is the additive group of a locally convex space, we describe all host algebras arising this way. The general non-commutative
case is left for the future.
To K.H. Hofmann on the occasion of his 75th birthday 相似文献
8.
A Hilbert C*-module is a generalization of a Hilbert space for which the inner
product takes its values in a C*-algebra instead of the complex numbers. We use the bracket
product to construct some Hilbert C*-modules over a group C*-algebra which is generated by the
group of translations associated with a wavelet. We shall investigate bracket products and their
Fourier transform in the space of square integrable functions in Euclidean space. We will also show
that some wavelets are associated with Hilbert C*-modules over the space of essentially bounded
functions over higher dimensional tori. 相似文献
9.
10.
L. Molnár 《Archiv der Mathematik》2000,74(2):120-128
We prove that the automorphism and isometry groups of any extension of the C*-algebra C (H)\cal C (\cal H) of all compact operators by a separable commutative C*-algebra are algebraically reflexive. Concerning the possibly most important extensions by the algebra C(\Bbb T)C(\Bbb T) of all continuous complex valued functions on the perimeter of the unit disc, we show that these groups are topologically nonreflexive. 相似文献
11.
Michael Frank 《Annals of Global Analysis and Geometry》1985,3(2):155-172
Let A be a C*-algebra, K be a compact space, A(K) be the C*-algebra of all continuous maps from K into A, 12(A) be the standard countably generated Hilbert A-module. We investigate a set of maps from K into EndA(12(A)), which is isomorphic to EndA(K)(12(A(K))). We describe the subsets which are isomorphic to EndfA(K)
*(12(A(K))). GLA(K)(12(A(K))) and GLfA(K)
*(12(A(K))), respectively. As an application we deduce a criterion for the self-duality of 12(A) in the commutative case. 相似文献
12.
《Comptes Rendus de l'Academie des Sciences Series IIA Earth and Planetary Science》1997,324(3):293-295
We show that the C* -algebra of the regular representation of a discrete group G onto a subset Σ of G is the reduced C* -algebra of an r-discrete groupoid whose space of units is totally disconnected and contains Σ as a dense subset. The C*-algebra of quasicrystals, some Cuntz-Krieger and crossed product algebras, and Wiener-Hopf algebras are particular cases of this construction 相似文献
13.
A generalization is given of the canonical map from a discrete group into K
1 of the group C
*-algebra. Our map also generalizes Rieffel's construction of a projection in an irrational rotation C
*-algebra. 相似文献
14.
We show that all rapid-decay locally compact groups are unimodular and that the set of rapid-decay functions on a locally compact rapidly decaying group forms a dense and spectral invariant Fréchet *-subalgebra of the reduced group C
*-algebra. In general, the set of rapid-decay functions on a locally compact strongly rapid-decay group with values in a commutative C
*-algebra forms a dense and spectral invariant Fréchet *-subalgebra of the twisted crossed product C
*-algebra. The spectral invariance property implies that the K-theories of both algebras are naturally isomorphic under inclusion.This project is supported in part by the National Science Foundation Grant #DMS 92-04005. 相似文献
15.
A pro-C*-algebra is a (projective) limit of C*-algebras in the category of topological *-algebras. From the perspective of non-commutative geometry, pro-C*-algebras can be seen as non-commutative k-spaces. An element of a pro-C*-algebra is bounded if there is a uniform bound for the norm of its images under any continuous *-homomorphism into a C*-algebra. The *-subalgebra consisting of the bounded elements turns out to be a C*-algebra. In this paper, we investigate pro-C*-algebras from a categorical point of view. We study the functor (−)
b
that assigns to a pro-C*-algebra the C*-algebra of its bounded elements, which is the dual of the Stone-Čech-compactification. We show that (−)
b
is a coreflector, and it preserves exact sequences. A generalization of the Gelfand duality for commutative unital pro-C*-algebras is also presented. 相似文献
16.
Subhash J Bhatt 《Proceedings Mathematical Sciences》1985,94(2-3):71-91
Consideration of quotient-bounded elements in a locally convexGB *-algebra leads to the study of properGB *-algebras viz those that admit nontrivial quotient-bounded elements. The construction and structure of such algebras are discussed. A representation theorem for a properGB *-algebra representing it as an algebra of unbounded Hilbert space operators is obtained in a form that unifies the well-known Gelfand-Naimark representation theorem forC *-algebra and two other representation theorems forb *-algebras (also calledlmc *-algebras), one representinga b *-algebra as an algebra of quotient bounded operators and the other as a weakly unbounded operator algebra. A number of examples are discussed to illustrate quotient-bounded operators. An algebra of unbounded operators constructed out of noncommutativeL p-spaces on a regular probability gauge space and the convolution algebra of periodic distributions are analyzed in detail; whereas unbounded Hilbert algebras andL w-integral of a measurable field ofC *-algebras are discussed briefly. 相似文献
17.
Eberhard Kirchberg 《Mathematische Nachrichten》1977,76(1):203-212
In this paper we show: A C*-algebra A with identity e is C*-nuclear (i.e. “nuclear” in the sense of LANCE [3, p. 159] or “property T” in the sense of TAKESAKI [6] if and only if the identity operator idA on A can be approximated in the strong operator topology by completely positive linear operators V from A into A of finite rank with norm one and V(e)=e. From which follows that every C*-nuclear C*-algebra (possible without identity) possesses the CPAP of LANCE [3, def. 3.5.]. This answers questions of LANCE [3, p. 173] and SAKAI [5, p. 64]. 相似文献
18.
19.
Chuanyi Zhang 《Journal of Fourier Analysis and Applications》2006,12(3):291-306
A new C*-algebra of strong limit power functions is proposed. The Gelfand space of the C*-algebra is endowed with an Abelian compact group structure. As applications of this, Fourier analysis and the Bochner-Fejér
approximation are carried out for a strong limit power function. Finally, the functions are extended to more general cases
and their properties are investigated in that settings. 相似文献
20.
Let be a domain with smooth boundary and let α be a C
2-
diffeomorphism on satisfying the Carleman condition .We denote
by the C*-algebra generated by the Bergman projection of G, all multiplication
operators aI and the operator where is the Jacobian of α. A symbol algebra of is determined and Fredholm
conditions are given. We prove that the C*-algebra generated by the Bergman
projection of the upper half-plane and the operator is isomorphic
and isometric to .
Submitted: February 11, 2001?Revised: January 27, 2002 相似文献