具有约当积性质的双线性映射

IF 1.1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications Pub Date : 2025-09-23 DOI:10.1016/j.laa.2025.09.013

Jorge J. Garcés , Mykola Khrypchenko

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引用次数: 0

摘要

研究了C -代数a上具有定元z∈a的Jordan积性质的对称连续双线性映射V。我们证明，当A是无限个简单冯·诺依曼代数的有限直和时，这样的映射V具有平方为零的性质。然后，证明了对于a上的某有界线性映射T， V(a,b)=T（a°b）。因此，刻画了z∈a上的Jordan同态和导数。

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Bilinear maps having Jordan product property

We study symmetric continuous bilinear maps V on a C^⁎ -algebra A that have the Jordan product property at a fixed element

z \in A

. We show that, whenever A is a finite direct sum of infinite simple von Neumann algebras, such a map V has the square-zero property. Then, it is proved that

V (a, b) = T (a \circ b)

for some bounded linear map T on A. As a consequence, Jordan homomorphisms and derivations at

z \in A

are characterized.

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来源期刊

Linear Algebra and its Applications 数学-应用数学

CiteScore

2.20

自引率

9.10%

发文量

333

审稿时长

13.8 months

期刊介绍： Linear Algebra and its Applications publishes articles that contribute new information or new insights to matrix theory and finite dimensional linear algebra in their algebraic, arithmetic, combinatorial, geometric, or numerical aspects. It also publishes articles that give significant applications of matrix theory or linear algebra to other branches of mathematics and to other sciences. Articles that provide new information or perspectives on the historical development of matrix theory and linear algebra are also welcome. Expository articles which can serve as an introduction to a subject for workers in related areas and which bring one to the frontiers of research are encouraged. Reviews of books are published occasionally as are conference reports that provide an historical record of major meetings on matrix theory and linear algebra.