共查询到20条相似文献,搜索用时 0 毫秒
1.
Ruy Exel 《K-Theory》1993,7(3):285-308
GivenC*-algebrasA andB and an imprimitivityA-B-bimoduleX, we construct an explicit isomorphismX
*:K
i
(A)K
i
(B), whereK
i
denotes the complexK-theory functors fori=0, 1. Our techniques do not require separability nor the existence of countable approximate identities. We thus extend to generalC*-algebras the result of Brown, Green, and Rieffel according to which, strongly Morita equivalentC*-algebras have isomorphicK-groups. The method employed includes a study of Fredholm operators on Hilbert modules.On leave from the University of São Paulo, Brazil. 相似文献
2.
Paul Jolissaint 《K-Theory》1989,2(6):723-735
We associate to any length function L on a group a space of rapidly decreasing functions on (in the l
2 sense), denoted by H
L
(). When H
L
() is contained in the reduced C*-algebra C
r
*
() of (), then it is a dense *-subalgebra of C
r
*
() and we prove a theorem of A. Connes which asserts that under this hypothesis H
L
() has the same K-theory as C
r
*
(). We introduce another space of rapidly decreasing functions on (in the l
1 sense), denoted by H
L
1,
(), which is always a dense *-subalgebra of the Banach algebra l
1(), and we show that H
L
1,
() has the same K-theory as l
1(). 相似文献
3.
For a certain class of extensions of C*-algebras in which B and A belong to classifiable classes of C*-algebras, we show that the functor which sends to its associated six term exact sequence in K-theory and the positive cones of K0(B) and K0(A) is a classification functor. We give two independent applications addressing the classification of a class of C*-algebras arising from substitutional shift spaces on one hand and of graph algebras on the other. The former application leads to the answer of a question of Carlsen and the first named author concerning the completeness of stabilized Matsumoto algebras as an invariant of flow equivalence. The latter leads to the first classification result for nonsimple graph C*-algebras. 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.
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
6.
Marius Dadarlat 《K-Theory》1995,9(2):117-137
It is shown that two unital *-homomorphisms from a commutativeC*-algebraC(X) to a unitalC*-algebraB are stably approximately unitarily equivalent if and only if they have the same class in the quotient of the Kasparov groupKK(C(X),B) by the closure of zero. A suitable generalization of this result is used to prove a classification result for certain inductive limitC*-algebrasThis research was partially supported by NSF grant DMS-9303361 相似文献
7.
8.
A new class of locally convex algebras, called BP*-algebras, is introduced. It is shown that this class properly includes MQ*-algebras which were introduced and studied by the first author andR. Rigelhof [10]. Among other results, it is proved that each positive functional on a BP*-algebraA is admissible but not necessarily continuous as shown by an example. However, ifA, in addition, is either (i) a Q-algebra, or (ii) has an identity and is barrelled, or (iii)A is endowed with the inductive limit topology, then each positive functional onA is continuous.This work was supported by an N.R.C. Grant. 相似文献
9.
In this paper, we point out that most results on abelian (complex)W
*-algebras hold in the real case. Of course, there are differences in homeomorphisms of period 2. Moreover, an abelian real
Von Neumann algebra not containing any minimal projection on a separable real Hilbert space is * isomorphic toL
τ
∞
([0, 1]) (all real functions inL
∞([0, 1])), orL
∞([0, 1]) (as a realW
*-algebra), orL
τ
∞
([0, 1]) ⋇L
∞ ([0, 1]) (as a realW
*-algebra), and it is different from the complex case.
Partially supported by the NNSF 相似文献
10.
Subhash J. Bhatt 《Proceedings Mathematical Sciences》2006,116(2):161-173
Given anm-tempered strongly continuous action α of ℝ by continuous*-automorphisms of a Frechet*-algebraA, it is shown that the enveloping ↡-C
*-algebraE(S(ℝ, A∞, α)) of the smooth Schwartz crossed productS(ℝ,A
∞, α) of the Frechet algebra A∞ of C∞-elements ofA is isomorphic to the Σ-C
*-crossed productC
*(ℝ,E(A), α) of the enveloping Σ-C
*-algebraE(A) ofA by the induced action. WhenA is a hermitianQ-algebra, one getsK-theory isomorphismRK
*(S(ℝ, A∞, α)) =K
*(C
*(ℝ,E(A), α) for the representableK-theory of Frechet algebras. An application to the differential structure of aC
*-algebra defined by densely defined differential seminorms is given. 相似文献
11.
V. M. Manuilov 《Mathematical Notes》2000,68(3):326-332
We study theC*-aglebras related to Mishchenko’s version of asymptotic homomorphisms. In particular, we show that their different versions
are weakly homotopy equivalent but not isomorphic to each other. We also present continuous versions of these algebras.
Translated fromMatematicheskie Zametki, Vol. 68, No. 3, pp. 377–384, September, 2000. 相似文献
12.
Stefano Cavallaro 《Algebras and Representation Theory》2000,3(2):175-186
Let
be an Abelian unital C
*-algebra and let
denote its Gelfand spectrum. We give some necessary and sufficient conditions for a nondegenerate representation of
to be unitarily equivalent to a representation in which the elements of
act multiplicatively, by their Gelfand transforms, on a space L
2(
,), where is a positive measure on the Baire sets of
. We also compare these conditions with the multiplicity-free property of a representation. 相似文献
13.
Let A be a separable simple C*-algebra. For each ;) on A such that π(a) has a non-trivial invariant subspace in Hπ. 相似文献
14.
Chunhong FU 《数学年刊B辑(英文版)》2023,44(3):325-344
Motivated by two norm equations used to characterize the Friedrichs angle, this paper studies C*-isomorphisms associated with two projections by introducing the matched triple and the semi-harmonious pair of projections. A triple (P, Q, H) is said to be matched if H is a Hilbert C*-module, P and Q are projections on H such that their infimum P ∧ Q exists as an element of L(H), where L(H) denotes the set of all adjointable operators on H. The C*-subalgebras of L(H) generated by elements in {P - P ∧ Q, Q - P ∧ Q, I} and {P, Q, P ∧ Q, I} are denoted by i(P, Q, H) and o(P, Q, H), respectively. It is proved that each faithful representation (π, X) of o(P, Q, H) can induce a faithful representation (π, X e) of i(P, Q, H) such that e π(P - P ∧ Q) = π(P) - π(P) ∧ π(Q),eπ(Q - P ∧ Q) = π(Q) - π(P) ∧ π(Q).When (P, Q) is semi-harmonious, that is, R(P + Q) and R(2I - P - Q) are both orthogonally complemented in H, it is shown that i(P, Q, H) and i(I - Q, I - P, H) are unitarily equivalent via a unitary operator in L(H). A counterexample is constructed, which shows that the same may be not true when (P, Q) fails to be semi-harmonious. Likewise, a counterexample is constructed such that (P, Q) is semi-harmonious, whereas (P, I - Q) is not semi-harmonious. Some additional examples indicating new phenomena of adjointable operators acting on Hilbert C*-modules are also provided. 相似文献
15.
Maria Joiţa 《Czechoslovak Mathematical Journal》2004,54(3):727-737
In this paper the tensor products of Hilbert modules over locally C
*-algebras are defined and their properties are studied. Thus we show that most of the basic properties of the tensor products of Hilbert C
*-modules are also valid in the context of Hilbert modules over locally C
*-algebras. 相似文献
16.
For any finite groupG we construct examples of an AF algebraA and an action byG onA such that the fixed point algebra is not AF. The construction ofA is done by successive foldings and cuttings of the interval in a way originally suggested by Blackadar and, in a different context, by Connes in his talk in Oslo in 1978. 相似文献
17.
Shuang Zhang 《K-Theory》1992,6(1):1-27
We first determine the homotopy classes of nontrivial projections in a purely infinite simpleC*-algebraA, in the associated multiplier algebraM(A) and the corona algebraM
A/A in terms ofK
*(A). Then we describe the generalized Fredholm indices as the group of homotopy classes of non-trivial projections ofA; consequently, we determine theK
*-groups of all hereditaryC*-subalgebras of certain corona algebras. Secondly, we consider a group structure of *-isomorphism classes of hereditaryC*-subalgebras of purely infinite simpleC*-algebras. In addition, we prove that ifA is aC*-algebra of real rank zero, then each unitary ofA, in caseA it unital, each unitary ofM(A) and ofM(A)/A, in caseA is nonunital but -unital, can be factored into a product of a unitary homotopic to the identity and a unitary matrix whose entries are all partial isometries (with respect to a decomposition of the identity).Partially supported by a grant from the National Science Foundation. 相似文献
18.
LunChuanZHANG 《数学学报(英文版)》2003,19(2):413-416
The relation between the inseparable prime C^*-algebras and primitive C^*-algebras is studied,and we prove that prime AW^*-algebras are all primitive C^*-algebras. 相似文献
19.
José M. Isidro 《Central European Journal of Mathematics》2007,5(3):512-522
Let G be the Banach-Lie group of all holomorphic automorphisms of the open unit ball
in a J*-algebra
of operators. Let
be the family of all collectively compact subsets W contained in
. We show that the subgroup F ⊂ G of all those g ∈ G that preserve the family
is a closed Lie subgroup of G and characterize its Banach-Lie algebra. We make a detailed study of F when
is a Cartan factor.
相似文献
20.
Shuang Zhang 《K-Theory》2001,24(3):203-225
We completely determine the homotopy groups
n
(.) of the unitary group and the space of projections of purely infinite simple C
*-algebras in terms of K-theory. We also prove that the unitary group of a purely infinite simple C
*-algebra A is a contractible topological space if and only if K0(A) = K1(A) = {0}, and again if and only if the unitary group of the associated generalized Calkin algebra L(HA) / K(HA) is contractible. The well-known Kuiper's theorem is extended to a new class of C
*-algebras. 相似文献