Crossed products by finite group actions with the Rokhlin property

We prove that a number of classes of separable unital C*-algebras are closed under crossed products by finite group actions with the Rokhlin property, including: (a) AI algebras, AT algebras, and related classes characterized by direct limit decompositions using semiprojective building blocks. (b) Simple unital AH algebras with slow dimension growth and real rank zero. (c) C*-algebras with real rank zero or stable rank one. (d) Simple C*-algebras for which the order on projections is determined by traces. (e) C*-algebras whose quotients all satisfy the Universal Coefficient Theorem. (f) C*-algebras with a unique tracial state. Along the way, we give a systematic treatment of the derivation of direct limit decompositions from local approximation conditions by homomorphic images which are not necessarily injective.     

Completely Positive Definite Maps on σ-C*-algebras

Recently,there has been increased interest[1-8]in topological*-algebras that are inverse     

A note on commutation relations and finite dimensional approximations

In this article we show that the main C*-algebras describing the canonical commutation relations of quantum physics, i.e., the Weyl and resolvent algebras, are in the class of Følner C*-algebras, a class of C*-algebras admitting a kind of finite approximations of Følner type. In particular, we show that the tracial states of the resolvent algebra are uniform locally finite dimensional.     

PrO-C*-代数的顺从性和核性

研究了Pro—C^*-代数的顺从性和核性．主要证明了(1)顺从Pro—C^*代数的闭理想是顺从的；(2)核Pro—C^*代数类对归纳极限封闭；(3)交换σ-C^*-代数和核C^*-代数都是核，σ-C^*-代数并且核σ-C^*-代数类对于商运算、张量积运算和可数逆向极限封闭．进一步得到核，σ-C^*-代数的扩张保持核性的条件。     

Spectral Properties of Partial *-Algebras

We continue our study of topological partial *algebras focusing our attention to some basic spectral properties. The special case of partial *-algebras of operators is examined first, in order to find sufficient hints for the study of the abstract case. The outcome consists in the selection of a class of topological partial *-algebras (partial GC*-algebras) that behave well from the spectral point of view and that allow, under certain conditions, a faithful realization as a partial O*-algebra.     

Entropy estimates for some C-endomorphisms

In this paper we compute the non-commutative topological entropy in the sense of Voiculescu for some endomorphisms of stationary inductive limits of circle algebras. These algebras are groupoid C*-algebras, and the endomorphisms restricted to the canonical diagonal are induced by some expansive maps, whose entropies provide a lower bound. For the upper bound, we use a result of Voiculescu, similar to the classical Kolmogorov-Sinai theorem. The same technique is used to compute the entropy of a non-commutative Markov shift.

     

The(**)-Haagerup Property for C*-Algebras

Extending the notion of Haagerup property for finite von Neumann algebras to the general von Neumann algebras, the authors define and study the(**)-Haagerup property for C*-algebras in this paper. They first give an answer to Suzuki's question(2013), and then obtain several results of(**)-Haagerup property parallel to those of Haagerup property for C*-algebras. It is proved that a nuclear unital C*-algebra with a faithful tracial state always has the(**)-Haagerup property. Some heredity results concerning the(**)-Haagerup property are also proved.     

On Some Problems Studied by R. V. Kadison

Several problems studied by professor R. V. Kadison are shown to be closely related. The problems were originally formulated in the contexts of homomorphisms of C^*-algebras, cohomology of von Neumann algebras and perturbations of C^*-algebras. Recent research by G. Pisier has demonstrated that all of the problems considered are related to the question of whether all C^*-algebras have finite length.     

C*-Bundles for Certain Liminal C*-Algebras

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.      

Toeplitz代数的上同调群

本文计算了Hardy空间上符号在H∞或C以及H∞＋C中的Toenlitz代数的上同调群．其结果说明,C*-代数的上同调群比VonNeumann代数的上同调群复杂．     

Active lattices determine AW*-algebras

We prove that operator algebras that have enough projections are completely determined by those projections, their symmetries, and the action of the latter on the former. This includes all von Neumann algebras and all AW*-algebras. We introduce active lattices, which are formed from these three ingredients. More generally, we prove that the category of AW*-algebras is equivalent to a full subcategory of active lattices. Crucial ingredients are an equivalence between the category of piecewise AW*-algebras and that of piecewise complete Boolean algebras, and a refinement of the piecewise algebra structure of an AW*-algebra that enables recovering its total structure.     

Morita equivalence of C*-correspondences passes to the related operator algebras

We revisit a central result of Muhly and Solel on operator algebras of C*-correspondences. We prove that (possibly non-injective) strongly Morita equivalent C*-correspondences have strongly Morita equivalent relative Cuntz–Pimsner C*-algebras. The same holds for strong Morita equivalence (in the sense of Blecher, Muhly and Paulsen) and strong Δ-equivalence (in the sense of Eleftherakis) for the related tensor algebras. In particular, we obtain stable isomorphism of the operator algebras when the equivalence is given by a σ-TRO. As an application we show that strong Morita equivalence coincides with strong Δ-equivalence for tensor algebras of aperiodic C*-correspondences.     

On action of diffeomorphisms of C*-algebras on derivations

In this paper we consider automorphisms of the domains of closed *-derivations of C*-algebras and show that they extend to automorphisms of C*-algebras, so we call them diffeomorphisms. The diffeomorphisms generate transformations of the sets of closed *-derivations of C*-algebras. In this paper we study the subgroups of diffeomorphisms that define “bounded” shifts of derivations and the subgroups of the stabilizers of derivations.     

Hilbert space representations of cross product algebras

Hilbert space representations of cross product *-algebras of the Hopf *-algebras with the coordinate algebras and of quantum vector spaces, and of with the coordinate algebras and of the corresponding quantum spheres, are investigated and classified. Invariant states on the coordinate *-algebras are described by two variants of the quantum trace.     

Covariant Projective Extensions

The theory of crossed products of C~*-algebras by groups of automorphisms is a well-developed area of the theory of operator algebras. Given the importance and the success ofthat theory, it is natural to attempt to extend it to a more general situation by, for example,developing a theory of crossed products of C~*-algebras by semigroups of automorphisms, or evenof endomorphisms. Indeed, in recent years a number of papers have appeared that are concernedwith such non-classical theories of covariance algebras, see, for instance [1-3].     

Positive Functionals on some Spaces of Fractions

The aim of this work is to study norm preserving extensions of positive functionals on some spaces of fractions. The main result is stated in the case of unitary complex Banach algebras with involution. Moreover, we deal with C*-algebras and the commutative case as well. An application is also given.     

Weak-local derivations and homomorphisms on C*-algebras

We prove that every weak-local derivation on a C*-algebra is continuous, and the same conclusion remains valid for weak*-local derivations on von Neumann algebras. We further show that weak-local derivations on C*-algebras and weak*-local derivations on von Neumann algebras are derivations. We also study the connections between bilocal derivations and bilocal*-automorphism with our notions of extreme-strong-local derivations and automorphisms.     

HANKEL OPERATORS AND HANKEL ALGEBRAS

ＨＡＮＫＥＬＯＰＥＲＡＴＯＲＳＡＮＤＨＡＮＫＥＬＡＬＧＥＢＲＡＳＹＡＮＳＨＡＯＺＯＮＧＣＨＥＮＸＩＡＯＭＡＮＧＵＯＫＵＮＹＵＭａｎｕｓｃｒｉｐｔｒｅｃｅｉｖｅｄＪｕｎｅ２３，１９９５．ＩｎｓｔｉｔｕｔｅｏｆＭａｔｈｅｍａｔｉｃｓ，Ｆｕｄａ...     

实厄米Banach*-代数

对任意实厄米的B anach*-代数进行系统研究,即对不需任何附加条件限制的代数进行研究,讨论方法与传统的假定代数具有单位元和*-运算是连续的两个重要假定条件下的方法不同.     

实Banach代数的表示

本文研究了对任意厄米实Banach*-代数的表示理论进行系统研究. 利用对该类代数所定义的一般态空间展开讨论. 获得了该类代数上可表示泛函的一系列好的性质,进而给出了不可约表示的等价刻画.这些结果将Naimark、Gaur等人的工作进行了推广.