共查询到20条相似文献,搜索用时 0 毫秒
1.
Let A and B be C*-algebras. A linear map T : A → B is said to be a *-homomorphism at an element z ∈ A if ab* = z in A implies T (ab*) = T (a)T (b)* = T (z), and c*d = z in A gives T (c*d) = T (c)*T (d) = T (z). Assuming that A is unital, we prove that every linear map T : A → B which is a *-homomorphism at the unit of A is a Jordan *-homomorphism. If A is simple and infinite, then we establish that a linear map T : A → B is a *-homomorphism if and only if T is a *-homomorphism at the unit of A. For a general unital C*-algebra A and a linear map T : A → B, we prove that T is a *-homomorphism if, and only if, T is a *-homomorphism at 0 and at 1. Actually if p is a non-zero projection in A, and T is a ?-homomorphism at p and at 1 ? p, then we prove that T is a Jordan *-homomorphism. We also study bounded linear maps that are *-homomorphisms at a unitary element in A. 相似文献
2.
We associate to each function algebra a C*-algebra and investigate
its properties. We are particularly interested in those of its properties that are
important for the Toeplitz operator theory on Hardy spaces of representing
measures of the function algebra. 相似文献
3.
Ghislain Vaillant 《Integral Equations and Operator Theory》1995,22(3):339-351
In this note we show that a separable C*-algebra is nuclear and has a quasidiagonal extension by
(the ideal of compact operators on an infinite-dimensional separable Hilbert space) if and only if it is anuclear finite algebra (NF-algebra) in the sense of Blackadar and Kirchberg, and deduce that every nuclear C*-subalgebra of aNF-algebra isNF. We show that strongNF-algebras satisfy a Følner type condition. 相似文献
4.
Xiaochun Fang 《Integral Equations and Operator Theory》2006,54(3):301-316
Let E be a possibly row-infinite directed graph. In this paper, first we prove the existence of the universal C*-algebra C*(E) of E which is generated by a Cuntz-Krieger E-family {se, pv}, and the gauge-invariant uniqueness theorem and the Cuntz-Krieger uniqueness theorem for the ideal
of C*(E). Then we get our main results about the ideal structure of
Finally the simplicity and the pure infiniteness of
is discussed. 相似文献
5.
We introduce a new asymptotic one-sided and symmetric tensor norm, the latter of which can be considered as the minimal tensor
norm on the category of separable C*-algebras with homotopy classes of asymptotic homomorphisms as morphisms. We show that the one-sided asymptotic tensor norm
differs in general from both the minimal and the maximal tensor norms and discuss its relation to semi-invertibility of C*-extensions.
Received: 23 September 2004; revised: 30 May 2005 相似文献
6.
Let
be a C*-algebra. We obtain some conditions that are equivalent to the statement that every n-positive elementary operator on
is completely positive. 相似文献
7.
8.
Aldo J. Lazar 《Integral Equations and Operator Theory》2008,60(3):381-404
It is shown that certain liminal C*-algebras whose limit sets in their primitive ideal space are discrete can be described as algebras of continuous sections
of a C*-bundle associated with them. Their multiplier algebras are also described in a similar manner. The class of C*-algebras under discussion includes all the liminal C*-algebras with Hausdorff primitive ideal spaces but also many other liminal algebras. A large sub-class of examples is examined
in detail.
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9.
10.
11.
Let M be a type I von Neumann algebra with the center Z, and a faithful normal semi-finite trace τ. Consider the algebra L(M, τ) of all τ-measurable operators with respect to M and let S
0(M, τ) be the subalgebra of τ-compact operators in L(M, τ). We prove that any Z-linear derivation of S
0(M, τ) is spatial and generated by an element from L(M, τ).
相似文献
12.
13.
We show that semigroup C*-algebras attached to ax+b-semigroups over rings of integers determine number fields up to arithmetic equivalence, under the assumption that the number fields have the same number of roots of unity. For finite Galois extensions, this means that the semigroup C*-algebras are isomorphic if and only if the number fields are isomorphic. 相似文献
14.
In this paper we define and study chain conditions for Hilbert C*-modules through their C*-algebras of compact operators and discuss their perseverance under Morita equivalence and tensor products. We show that these chain conditions are passed from the C*-algebra to its Hilbert module under certain conditions. We also study chain conditions for Hilbert modules coming from inclusion of C*-algebra with a faithful conditional expectation. 相似文献
15.
Masayoshi Kaneda 《Journal of Functional Analysis》2007,251(1):346-359
Let X be an operator space, let φ be a product on X, and let (X,φ) denote the algebra that one obtains. We give necessary and sufficient conditions on the bilinear mapping φ for the algebra (X,φ) to have a completely isometric representation as an algebra of operators on some Hilbert space. In particular, we give an elegant geometrical characterization of such products by using the Haagerup tensor product. Our result makes no assumptions about identities or approximate identities. Our proof is independent of the earlier result of Blecher, Ruan and Sinclair [D.P. Blecher, Z.-J. Ruan, A.M. Sinclair, A characterization of operator algebras, J. Funct. Anal. 89 (1) (1990) 188-201] which solved the case when the bilinear mapping has an identity of norm one, and our result is used to give a simple direct proof of this earlier result. We also develop further the connections between quasi-multipliers of operator spaces and their representations on a Hilbert space or their embeddings in the second dual, and show that the quasi-multipliers of operator spaces defined in [M. Kaneda, V.I. Paulsen, Quasi-multipliers of operator spaces, J. Funct. Anal. 217 (2) (2004) 347-365] coincide with their C∗-algebraic counterparts. 相似文献
16.
Congquan Yan 《Integral Equations and Operator Theory》2006,56(4):587-595
In this paper, we obtain a Fredholm index formula for Toeplitz operators whose symbols are certain piecewise continuous function
matrices on the unit ball. Moreover, using this formula, we discuss the automorphisms on the corresponding Toeplitz algebra 相似文献
17.
The possibility of extending the well known Gelfand–Naimark–Segal representation of *-algebras to certain Banach C*-modules is studied. For this aim the notion of modular biweight on a Banach C*-module is introduced. For the particular class of strict pre CQ*-algebras, two different types of representations are investigated. 相似文献
18.
Jean-Pierre Antoine Camillo Trapani Francesco Tschinke 《Mediterranean Journal of Mathematics》2007,4(3):357-373
We continue the study of Banach partial *-algebras, in particular the question of the interplay between *-homomorphisms and
biweights. Two special types of objects are introduced, namely, relatively bounded biweights and Banach partial *-algebras
satisfying a certain Condition (S), which behave in a more regular way. We also present a systematic construction of Banach
partial *-algebras of this type and exhibit several examples. 相似文献
19.
In this review we describe the basic structure of positive continuous one-parameter semigroups acting on ordered Banach spaces. The review is in two parts.First we discuss the general structure of ordered Banach spaces and their ordered duals. We examine normality and generation properties of the cones of positive elements with particular emphasis on monotone properties of the norm. The special cases of Banach lattices, order-unit spaces, and base-norm spaces, are also examined.Second we develop the theory of positive strongly continuous semigroups on ordered Banach spaces, and positive weak*-continuous semigroups on the dual spaces. Initially we derive analogues of the Feller-Miyadera-Phillips and Hille-Yosida theorems on generation of positive semigroups. Subsequently we analyse strict positivity, irreducibility, and spectral properties, in parallel with the Perron-Frobenius theory of positive matrices. 相似文献
20.
Ruey-Jen Jang-Lewis Harold Dean Victory Jr. 《Integral Equations and Operator Theory》1994,18(1):88-108
LetE be a Banach lattice having order continuous norm. Suppose, moreover,T is a nonnegative reducible operator having a compact iterate and which mapsE into itself. The purpose of this work is to extend the previous results of the authors, concerning nonnegative solvability of (kernel) operator equations on generalL
p-spaces. In particular, we provide necessary and sufficient conditions for the operator equation x=T
x+y to possess a nonnegative solutionxE wherey is a given nonnegative and nontrivial element ofE and is any given positive parameter. 相似文献