共查询到20条相似文献,搜索用时 31 毫秒
1.
Chun-Gil Park 《Journal of Mathematical Analysis and Applications》2005,307(2):753-762
It is shown that every almost linear bijection of a unital C∗-algebra A onto a unital C∗-algebra B is a C∗-algebra isomorphism when h(n2uy)=h(n2u)h(y) for all unitaries u∈A, all y∈A, and n=0,1,2,…, and that almost linear continuous bijection of a unital C∗-algebra A of real rank zero onto a unital C∗-algebra B is a C∗-algebra isomorphism when h(n2uy)=h(n2u)h(y) for all , all y∈A, and n=0,1,2,…. Assume that X and Y are left normed modules over a unital C∗-algebra A. It is shown that every surjective isometry , satisfying T(0)=0 and T(ux)=uT(x) for all x∈X and all unitaries u∈A, is an A-linear isomorphism. This is applied to investigate C∗-algebra isomorphisms between unital C∗-algebras. 相似文献
2.
Cornel Pasnicu 《Journal of Mathematical Analysis and Applications》2006,323(2):1213-1224
Let A be the C∗-algebra associated to an arbitrary continuous field of C∗-algebras. We give a necessary and sufficient condition for A to have the ideal property and, if moreover A is separable, we give a necessary and sufficient condition for A to have the projection property. Some applications of these results are given. We also prove that “many” crossed products of commutative C∗-algebras by discrete, amenable groups have the projection property, generalizing some of our previous results. 相似文献
3.
Takeshi Katsura 《Journal of Functional Analysis》2009,257(5):1589-127
We give various necessary and sufficient conditions for an AF-algebra to be isomorphic to a graph C∗-algebra, an Exel-Laca algebra, and an ultragraph C∗-algebra. We also explore consequences of these results. In particular, we show that all stable AF-algebras are both graph C∗-algebras and Exel-Laca algebras, and that all simple AF-algebras are either graph C∗-algebras or Exel-Laca algebras. In addition, we obtain a characterization of AF-algebras that are isomorphic to the C∗-algebra of a row-finite graph with no sinks. 相似文献
4.
We discuss the representation theory of both the locally convex and non-locally convex topological*-algebras. First we discuss the*-representation of topological*-algebras by operators on a Hilbert space. Then we study those topological*-algebras so that every*-representation of which on a Hilbert space is necessarily continuous. It is well-known that each*-representation of aB
*-algebra on a Hilbert space is continuous. We show that this is true for a large class of*-algebras more general thanB
*-algebras, including certain non-locally convex*-algebras. Finally, we investigate the conditions under which a positive functional on a topological*-algebra is representable.The research of the first-named author was partially supported by an NSERC grant. This work was done by the second-named author when he was a post-doctoral fellow at McMaster University. 相似文献
5.
Jung-Hui Liu 《Journal of Mathematical Analysis and Applications》2006,321(2):741-750
A not necessarily continuous, linear or multiplicative function θ from an algebra A into itself is called a 2-local automorphism if θ agrees with an automorphism of A at each pair of points in A. In this paper, we study when a 2-local automorphism of a C∗-algebra, or a standard operator algebra on a locally convex space, is an automorphism. 相似文献
6.
Marina Haralampidou Reyna María Pérez-Tiscareño 《Mediterranean Journal of Mathematics》2013,10(1):411-424
We introduce (left, right, two-sided) locally convex H*-algebras, and we give conditions under which an one-sided locally convex H*-algebra turns to be a two-sided one (actually, a locally convex H*-algebra). We also give an example of a proper right locally convex H*-algebra with a (right) involution, which is not a left involution and an example of a proper two-sided locally convex H*-algebra, which is not a locally convex H*-algebra. Moreover, we connect (via an Arens-Michael decomposition) a two-sided locally m-convex H*-algebra with the classical (Banach) two-sided H*-algebras. Further, we present conditions so that the left, right involutions be continuous, and we see when a twosided locally convex H*-algebra is a dual one. Finally, we present some properties of invariant ideals which play an important rôle in structure theory of two-sided locally convex H*-algebras. 相似文献
7.
Jakob Cimprič 《Positivity》2011,15(3):481-495
We study non-commutative real algebraic geometry for a unital associative *-algebra A{\mathcal {A}} viewing the points as pairs (π, v) where π is an unbounded *-representation of A{\mathcal A} on an inner product space which contains the vector v. We first consider the *-algebras of matrices of usual and free real multivariate polynomials with their natural subsets
of points. If all points are allowed then we can obtain results for general A{\mathcal {A}}. Finally, we compare our results with their analogues in the usual (i.e. Schmüdgen’s) non-commutative real algebraic geometry
where the points are unbounded *-representation of A{\mathcal {A}}. 相似文献
8.
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
9.
It is shown that if A is a stably finite C∗-algebra and E is a countably generated Hilbert A-module, then E gives rise to a compact element of the Cuntz semigroup if and only if E is algebraically finitely generated and projective. It follows that if E and F are equivalent in the sense of Coward, Elliott and Ivanescu (CEI) and E is algebraically finitely generated and projective, then E and F are isomorphic. In contrast to this, we exhibit two CEI-equivalent Hilbert modules over a stably finite C∗-algebra that are not isomorphic. 相似文献
10.
Jeffrey L. Boersema 《Journal of Functional Analysis》2006,235(2):702-718
We prove that the united K-theory functor is a surjective functor from the category of real simple separable purely infinite C∗-algebras to the category of countable acyclic CRT-modules. As a consequence, we show that every complex Kirchberg algebra satisfying the universal coefficient theorem is the complexification of a real C∗-algebra. 相似文献
11.
Bojan Magajna 《Journal of Mathematical Analysis and Applications》2008,342(2):1481-1484
A unital C∗-algebra A is weakly central if and only if for every x∈A there exists a sequence of elementary unital completely positive maps αn on A such that the sequence (αn(x)) converges to a central element. 相似文献
12.
Kenneth R. Davidson Stephen C. Power Dilian Yang 《Journal of Functional Analysis》2008,255(4):819-853
We provide a detailed analysis of atomic ∗-representations of rank 2 graphs on a single vertex. They are completely classified up to unitary equivalence, and decomposed into a direct sum or direct integral of irreducible atomic representations. The building blocks are described as the minimal ∗-dilations of defect free representations modelled on finite groups of rank 2. 相似文献
13.
Erling Størmer 《Journal of Functional Analysis》2008,254(8):2303-2312
Using the natural duality between linear functionals on tensor products of C∗-algebras with the trace class operators on a Hilbert space H and linear maps of the C∗-algebra into B(H), we study the relationship between separability, entanglement and the Peres condition of states and positivity properties of the linear maps. 相似文献
14.
Alexander Alldridge 《Journal of Functional Analysis》2007,249(2):425-453
We study multivariate generalisations of the classical Wiener-Hopf algebra, which is the C∗-algebra generated by the Wiener-Hopf operators, given by convolutions restricted to convex cones. By the work of Muhly and Renault, this C∗-algebra is known to be isomorphic to the reduced C∗-algebra of a certain restricted action groupoid, given by the action of Euclidean space on a certain compactification. Using groupoid methods, we construct composition series for the Wiener-Hopf C∗-algebra by a detailed study of this compactification. We compute the spectrum, and express homomorphisms in K-theory induced by the symbol maps which arise by the subquotients of the composition series in analytical terms. Namely, these symbols maps turn out to be given by an analytical family index of a continuous family of Fredholm operators. In a subsequent paper, we also obtain a topological expression of these indices. 相似文献
15.
Dijana Mosi? Dragan S. Djordjevi? 《Applied mathematics and computation》2012,218(9):5383-5390
We present characterizations of weighted-EP elements in C∗-algebras using different kinds of factorizations. 相似文献
16.
Lajos Molnár 《Journal of Mathematical Analysis and Applications》2007,327(1):302-309
Let H be a Hilbert space and let A and B be standard ∗-operator algebras on H. Denote by As and Bs the set of all self-adjoint operators in A and B, respectively. Assume that and are surjective maps such that M(AM∗(B)A)=M(A)BM(A) and M∗(BM(A)B)=M∗(B)AM∗(B) for every pair A∈As, B∈Bs. Then there exist an invertible bounded linear or conjugate-linear operator and a constant c∈{−1,1} such that M(A)=cTAT∗, A∈As, and M∗(B)=cT∗BT, B∈Bs. 相似文献
17.
Maria Fragoulopoulou 《Journal of Mathematical Analysis and Applications》1985,108(2):422-429
The classical transitivity theorem of R. Kadison for C1-algebras is here extended to the case of a locally C1-algebra E. As a consequence, within the same context, various standard facts referred to the space of representations of E are obtained, broadening thus naturally out an earlier framework considered by this author, the relevant results being namely obtained hitherto only for bQ locally m-convex 1-algebras. 相似文献
18.
Najla A. Altwaijry 《Journal of Functional Analysis》2008,254(11):2866-2892
The Banach-Lie algebra L(A) of multiplication operators on the JB∗-triple A is introduced and it is shown that the hermitian part Lh(A) of L(A) is a unital GM-space the base of the dual cone in the dual GL-space ∗(Lh(A)) of which is affine isomorphic and weak∗-homeomorphic to the state space of L(A). In the case in which A is a JBW∗-triple, it is shown that tripotents u and v in A are orthogonal if and only if the corresponding multiplication operators in the unital GM-space Lh(A) satisfy
0?D(u,u)+D(v,v)?idA, 相似文献
19.
Xiu-Chi Quan 《Acta Appl Math》1991,25(3):277-299
In this paper, we consider the *-representations of compact quantum groups and group duality. The main results in the paper are: (1) there is a one-to-one correspondence between the *-representations of compact quantum groups and *-representations of the dual Banach *-algebra; (2) the category of commutative compact quantum groups (semigroups) is a dual category to the category of compact groups (semigroups); (3) the dual category of the category of locally compact groups (semigroups) is the category of commutative Hopf C*-algebras with a particular property. Our group duality has the flavor of a Gelfand-Naimark type theorem for compact quantum groups, and for Hopf C*-algebras. 相似文献
20.
We prove the following: Let A and B be separable C*-algebras. Suppose that B is a type I C*-algebra such that
- (i)
- B has only infinite dimensional irreducible *-representations, and
- (ii)
- B has finite decomposition rank.
0→B→C→A→0 相似文献