共查询到20条相似文献,搜索用时 31 毫秒
1.
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. 相似文献
2.
This paper studies the spaces of Gateaux and Frechet Operator
Differentiable functions of a real variable and their link with the space of Operator
Lipschitz functions. Apart from the standard operator norm on B(H),
we consider a rich variety of spaces of Operator Differentiable and Operator
Lipschitz functions with respect to symmetric operator norms. Our approach
is aimed at the investigation of the interrelation and hierarchy of these spaces
and of the intrinsic properties of Operator Differentiable functions. We apply
the obtained results to the study of the functions acting on the domains
of closed *-derivations of C*-algebras and prove that Operator Differentiable
functions act on all such domains.We also obtain the following modification of
this result: any continuously differentiable, Operator Lipschitz function acts
on the domains of all weakly closed *-derivations of C*-algebras. 相似文献
3.
R. Becker 《Mathematische Nachrichten》1992,155(1):141-149
It is shown that derivations on LMC*-algebras are always continuous and generate a continuous one-parameter group of automorphisms. The structure of the derivation and the automorphism group on LMC*-algebras is investigated. 相似文献
4.
Unbounded derivations in uniformly hyperfinite C1-algebras will be studied. Various conditions, under which normal 1-derivations in the C1-algebras can be extended to the infinitesimal generators of the approximately inner strongly continuous one-parameter subgroups of 1-automorphisms on the algebras, will be given. 相似文献
5.
Using fixed point methods, we prove the Hyers-Ulam-Rassias stability and superstability of Jordan homomorphisms (Jordan *-homomorphisms), and Jordan derivations (Jordan *-derivations) on Banach algebras (C*-algebras) for the generalized Jensen-type functional equationwhere r is a fixed positive real number in (1, ∞). 相似文献
6.
In this paper,first,we consider closed convex and bounded subsets of infinite-dimensional unital Banach algebras and show with regard to the general conditions that these sets are not quasi-Chebyshev and pseudo-Chebyshev.Examples of those algebras are given including the algebras of continuous functions on compact sets.We also see some results in C*-algebras and Hilbert C*-modules.Next,by considering some conditions,we study Chebyshev of subalgebras in C*-algebras. 相似文献
7.
8.
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]. 相似文献
9.
10.
In this paper we find invariant subspaces of certain positive quasinilpotent operators on Krein spaces and, more generally,
on ordered Banach spaces with closed generating cones. In the later case, we use the method of minimal vectors. We present
applications to Sobolev spaces, spaces of differentiable functions, and C*-algebras.
相似文献
11.
Edward Kissin 《Journal of Functional Analysis》2006,232(1):56-89
The paper studies unbounded reflexive *-derivations δ of C*-algebras of bounded operators on Hilbert spaces H whose domains D(δ) are weekly dense in B(H and contain compact operators. It describes a one-to-one correspondence between these derivations and pairs S,L, where S are symmetric densely operators on H and L are J-orthogonal π-reflexive lattices of subspaces in the deficiency spaces of S. The domains D(δ) of these *-derivations are associated with some non-selfadjoint reflexive algebras Aδ of bounded operators on H⊕H. The paper analyzes the structure of the lattices of invariant subspaces of Aδ and of the normalizers of Aδ-the largest Lie subalgebras of B(H⊕H) such that Aδ are their Lie ideals. 相似文献
12.
13.
《Quaestiones Mathematicae》2013,36(2):241-256
Abstract Given a C*-algebra A and a suitable set of derivations on A, we consider the algebras A n of n-differentiable elements of A as described in [B], before passing to an analysis of important classes of bounded linear maps between two such spaces. We show that even in this general framework, all the main features of the theory for the case C(m)(U) → C (p) (V) where U and V are open balls in suitable Banach spaces, are preserved (see for example [A-G-L], [Gu-L], [Ja] and [L]). As part of the theory developed we obtain a non-trivial extension of the Kleinecke-Shirokov theorem in the category of C*-algebras to unbounded partially defined *-derivations. This indicates the existence of a single mathematical principle governing both the non-increasibility of differentiability by continuous homomorphisms and the untenability of the Heisenberg Uncertainty Principle for bounded observables. 相似文献
14.
Dijana Ilisevic Sanja Varosanec 《Proceedings of the American Mathematical Society》2005,133(11):3271-3280
In this paper we give some properties of a generalized inner product in modules over H*-algebras and C*-algebras and we obtain inequalities of Grüss type.
15.
N. Christopher Phillips 《Israel Journal of Mathematics》2007,160(1):189-217
We give examples of minimal diffeomorphisms of compact connected manifolds which are not topologically orbit equivalent, but
whose transformation group C*-algebras are isomorphic. The examples show that the following properties of a minimal diffeomorphism
are not invariants of the transformation group C*-algebra: having topologically quasidiscrete spectrum; the action on singular
cohomology (when the manifolds are diffeomorphic); the homotopy type of the manifold (when the manifolds have the same dimension);
and the dimension of the manifold.
These examples also give examples of nonconjugate isomorphic Cartan subalgebras, and of nonisomorphic Cartan subalgebras,
of simple separable nuclear unital C*-algebras with tracial rank zero and satisfying the Universal Coefficient Theorem.
The research was partially supported by the NSF grants DMS 9706850, DMS 0070776, DMS 0302401, and by the MSRI. 相似文献
16.
《Expositiones Mathematicae》2022,40(4):947-960
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. 相似文献
17.
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. 相似文献
18.
Let C be a class of unital C*-algebras. The class TAC of C*-algebras which can be tracially approximated (in the Egorov-like sense first considered by Lin) by the C*-algebras in C is studied (Lin considered the case that C consists of finite-dimensional C*-algebras or the tensor products of such with C([0,1])). In particular, the question is considered whether, for any simple separable A∈TAC, there is a C*-algebra B which is a simple inductive limit of certain basic homogeneous C*-algebras together with C*-algebras in C, such that the Elliott invariant of A is isomorphic to the Elliott invariant of B. An interesting case of this question is answered. In the final part of the paper, the question is also considered which properties of C*-algebras are inherited by tracial approximation. (Results of this kind are obtained which are used in the proof of the main theorem of the paper, and also in the proof of the classification theorem of the second author given in [Z. Niu, A classification of tracially approximately splitting tree algebra, in preparation] and [Z. Niu, A classification of certain tracially approximately subhomogeneous C*-algebras, PhD thesis, University of Toronto, 2005]—which also uses the main result of the present paper.) 相似文献
19.
C*-代数的*-同构一定是(完全)等距映射,反之不然.本文证明了C*-代数的实完全等距映射能够完全决定C*-代数*-同构的结论. 相似文献
20.
We obtain conditions on (R,+) which force that the zero map is the only derivation on a zero-symmetric near-ring R. Throughout the paper we construct several new examples of near-rings which are not rings admitting non-zero derivations, non-zero (σ, σ)-derivations and non-zero (1, σ)-derivations. 相似文献