标准算子代数上的Jordan *-导数

Pub Date : 2023-01-01 DOI:10.2298/fil2301037a

A. Ansari, F. Shujat

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引用次数: 0

摘要

LetH是一个实数或复希尔伯特空间，其中dim(H) >1, B(H)是H和a (H)上所有有界线性算子的代数?B(H)是H上的标准算子代数，如果D: a (H) ?B(H)是一个线性映射，满足D(An+1) = Pn i=0 AiD(a)(a *)n?i for all A ?A(H)那么D是A(H)的约当导数。随后，我们讨论了半素环上的一些代数恒等式。

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Jordan *-derivations on standard operator algebras

LetH be a real or complex Hilbert space with dim(H) > 1, B(H) be algebra of all bounded linear operators on H and A(H) ? B(H) be a standard operator algebra on H. If D : A(H) ? B(H) is a linear mapping satisfying D(An+1) = Pn i=0 AiD(A)(A*)n?i for all A ? A(H), then D is a Jordan *-derivation on A(H). Later, we discuss some algebraic identities on semiprime rings.

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