Quotients of Banach algebras acting on $L^p$-spaces

Abstract

We show that the class of Banach algebras that can be isometrically represented on an $L^p$-space, for $p\ne 2$, is not closed under quotients. This answers a question asked by Le Merdy 20 years ago. Our methods are heavily reliant on our earlier study of Banach algebras generated by invertible isometries of $L^p$-spaces.

6 pages. Version 2: minor modifications. To appear in Advances in Math

References in corpus (2)

• Column and row operator spaces over QSL_p-spaces and their use in abstract harmonic analysis
• Functoriality of group algebras acting on $L^p$-spaces

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