共查询到20条相似文献,搜索用时 46 毫秒
1.
Pere Ara 《K-Theory》1991,5(3):281-292
We give an explicit index map for any properly infinite closed ideal of a Rickart C
*-algebra. This generalizes Olsen's work on von Neumann algebras. We use our results to compute the topological and the algebraic K
1-groups of any quotient algebra of a Rickart C
*-algebra. 相似文献
2.
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
3.
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
4.
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
5.
N. Christopher Phillips 《Mathematische Nachrichten》1995,176(1):243-247
We prove the following two improvements of a result of Becker. (1) If A is a pro-C*-algebra, then every derivation on A is approximately inner. (2) If A is a separable σ-C*-algebra, and if every C* quotient of A has the property that every derivation on it is inner, then also every derivation on A is inner. We also give an example of a derivation on a separable σ-C*-algebra which is not inner but which induces an inner derivation on every C* quotient. 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.
8.
Abdellah El Kinani 《Rendiconti del Circolo Matematico di Palermo》2008,57(2):229-238
We endow any proper A-convex H*-algebra (E, τ) with a locally pre-C*-topology. The latter is equivalent to that introduced by the pre C*-norm given by Ptàk function when (E, τ) is a Q-algebra. We also prove that the algebra of complex numbers is the unique proper locally A-convex H*-algebra which is barrelled and Q-algebra.
相似文献
9.
We prove that a graph C
*-algebra with exactly one proper nontrivial ideal is classified up to stable isomorphism by its associated six-term exact
sequence in K-theory. We prove that a similar classification also holds for a graph C
*-algebra with a largest proper ideal that is an AF-algebra. Our results are based on a general method developed by the first
named author with Restorff and Ruiz. As a key step in the argument, we show how to produce stability for certain full hereditary
subalgebras associated to such graph C
*-algebras. We further prove that, except under trivial circumstances, a unique proper nontrivial ideal in a graph C
*-algebra is stable. 相似文献
10.
11.
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
12.
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
13.
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
14.
A C*-algebra generated by a commuting family of isometries is a natural generalization of the Toeplitz algebra. We study the
*-automorphisms and invariant ideals of the C*-algebra geerated by a semigroup. 相似文献
15.
Jeffrey L. BOERSEMA 《数学学报(英文版)》2007,23(10):1827-1832
We prove analogs of the Kaplansky Density Theorem and the Kadison Transitivity Theorem for irreducible representations of a real C*-algebra on a real Hilbert space. Specifically, if a C*-algebra is acting irreducibly on a real Hilbert space, then the Hilbert space has either a real, complex, or quaternionic structure with respect to which the density and transitivity theorems hold. 相似文献
16.
We show that a ring homomorphism from a local σ-C*-algebra to a local C*-algebra is a continuous mapping. 相似文献
17.
Kengo Matsumoto 《Mathematische Zeitschrift》2010,265(4):735-760
A C*-symbolic dynamical system ${(\mathcal{A}, \rho, \Sigma)}A C*-symbolic dynamical system (A, r, S){(\mathcal{A}, \rho, \Sigma)} consists of a unital C*-algebra A{\mathcal{A}} and a finite family { ra }a ? S{\{ \rho_\alpha \}_{\alpha \in \Sigma}} of endomorphisms ρ
α
of A{\mathcal{A}} indexed by symbols α of Σ satisfying some conditions. The endomorphisms ra, a ? S{\rho_\alpha, \alpha \in \Sigma } yield both a subshift Λ and a C*-algebra of a Hilbert C*-bimodule. The obtained C*-algebra is regarded as a crossed product of A{\mathcal{A}} by the subshift Λ. We will study simplicity condition of these C*-algebras. Some examples such as irrational rotation Cuntz–Krieger algebras will be studied. 相似文献
18.
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
19.
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
20.
Thomas L. Kriete Barbara D. MacCluer Jennifer L. Moorhouse 《Journal of Functional Analysis》2009,257(8):2378-2409
We determine the essential spectra of algebraic combinations of Toeplitz operators with continuous symbol and composition operators induced by a class of linear-fractional non-automorphisms of the unit disk. The operators in question act on the Hardy space H2 on the unit disk. Our method is to realize the C*-algebra that they generate as an extension of the compact operators by a concrete C*-algebra whose invertible elements are easily characterized. 相似文献