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arXiv · 1902.04846

Zero Jordan product determined Banach algebras

J. Alaminos·M. Brešar·J. Extremera·A. R. Villena
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Abstract

A Banach algebra $A$ is said to be a zero Jordan product determined Banach algebra if every continuous bilinear map $\varphi\colon A\times A\to X$, where $X$ is an arbitrary Banach space, which satisfies $\varphi(a,b)=0$ whenever $a$, $b\in A$ are such that $ab+ba=0$, is of the form $\varphi(a,b)=\sigma(ab+ba)$ for some continuous linear map $\sigma$. We show that all $C^*$-algebras and all group algebras $L^1(G)$ of amenable locally compact groups have this property, and also discuss some applications.

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J. Alaminos, M. Brešar, J. Extremera, A. R. Villena. 2019-02-13. Zero Jordan product determined Banach algebras. https://doi.org/10.1017/s1446788719000478

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