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1.
Bilocal derivations of standard operator algebras   总被引：5，自引：0，他引：5
In this paper, we shall show the following two results: (1) Let be a standard operator algebra with , if is a linear mapping on which satisfies that maps into for all , then is of the form for some in . (2) Let be a Hilbert space, if is a norm-continuous linear mapping on which satisfies that maps into for all self-adjoint projection in , then is of the form for some in .
2.
Local derivations of reflexive algebras   总被引：3，自引：0，他引：3
Let be a reflexive algebra in Banach space such that both and in , the invariant subspace lattice of , then every derivation of into itself is spatial. Furthermore, if is additionally reflexive, then the set of all inner derivations of into itself is topologically algebraically reflexive.
3.

4.
We show that for a locally compact group , every completely bounded local derivation from the Fourier algebra into a symmetric operator -module or the operator dual of an essential -bimodule is a derivation. Moreover, for amenable we show that the result is true for all operator -bimodules. In particular, we derive a new proof to a result of N. Spronk that is always operator weakly amenable.
5.
It is shown that continuous -local derivations on -algebras are derivations and surjective -local *-automorphisms on prime -algebras or on -algebras such that the identity element is properly infinite are *-automorphisms.
6.
In this paper, we introduce the concept of T-local derivations and obtain the main result: each T-local derivation of a von Neumann algebra A into a dual A-bimodule M is a T-derivation, where T is an endomorphism of A to A.  相似文献
7.
The aim of this note is to give a short proof that 2-local derivations on , the matrix algebra over the complex numbers are derivations and to give a shorter proof that 2-local *-automorphisms on are *-automorphisms.
8.

Let be a reflexive algebra in Banach space such that both and in Lat . Then every local derivation of into itself is a derivation.

9.
Given a spectrum X, we construct a spectral sequence of BP*BP-comodulesthat converges to BP*(LnX), where LnX is the Bousfield localizationof X with respect to the Johnson–Wilson theory E(n)*.The E2-term of this spectral sequence consists of the derivedfunctors of an algebraic version of Ln. We show how to calculatethese derived functors, which are closely related to local cohomologyof BP*-modules with respect to the ideal In+1. 2000 MathematicsSubject Classification 55N22, 55P60, 16W30.  相似文献
10.
We study certain commutative regular semisimple Banach algebras which we call hyper-Tauberian algebras. We first show that they form a subclass of weakly amenable Tauberian algebras. Then we investigate the basic and hereditary properties of them. Moreover, we show that if A is a hyper-Tauberian algebra, then the linear space of bounded derivations from A into any Banach A-bimodule is reflexive. We apply these results to the Figà-Talamanca-Herz algebra Ap(G) of a locally compact group G for p∈(1,∞). We show that Ap(G) is hyper-Tauberian if the principal component of G is abelian. Finally, by considering the quantization of these results, we show that for any locally compact group G, Ap(G), equipped with an appropriate operator space structure, is a quantized hyper-Tauberian algebra. This, in particular, implies that Ap(G) is operator weakly amenable.  相似文献
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