Geodesic
Zero Lie product determined Banach algebras
Studia Mathematica, Tome 239 (2017) no. 2, pp. 189-199 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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A Banach algebra $A$ is said to be zero Lie product determined if every continuous bilinear functional $\varphi \colon A\times A\to \mathbb {C}$ with $\varphi (a,b)=0$ whenever $a$ and $b$ commute is of the form $\varphi (a,b)=\tau (ab-ba)$ for some $\tau \in A^*$. In the first part of the paper we give some general remarks on this class of algebras. In the second part we consider amenable Banach algebras and show that all group algebras $L^1(G)$ with $G$ an amenable locally compact group are zero Lie product determined.
DOI : 10.4064/sm8734-4-2017
Keywords: banach algebra said zero lie product determined every continuous bilinear functional varphi colon times mathbb varphi whenever commute form varphi tau ab ba tau * first part paper general remarks class algebras second part consider amenable banach algebras group algebras amenable locally compact group zero lie product determined 
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     title = {Zero {Lie} product determined {Banach} algebras},
     journal = {Studia Mathematica},
     pages = {189--199},
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     doi = {10.4064/sm8734-4-2017},
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J. Alaminos; M. Brešar; J. Extremera; A. R. Villena. Zero Lie product determined Banach algebras. Studia Mathematica, Tome 239 (2017) no. 2, pp. 189-199. doi: 10.4064/sm8734-4-2017

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