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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 .

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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.

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3.
AF C~*-代数中的子代数上的保幂等映射和局部导子   总被引:2,自引:0,他引:2       下载免费PDF全文
纪培胜 《数学学报》1999,42(1):151-154
证明了从AFC-代数E中的子代数A到任意赋范代数B上的范数连续保幂等映射是Jordan同态,以及从A到任意赋范E-双模M上的局部导子是导子,从而推广了Crist关于局部导子的结果.  相似文献
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.

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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.

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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.

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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.

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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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