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

Published 12 Dec 2014 in math.OA and math.FA | (1412.3985v2)

Abstract: We show that the class of Banach algebras that can be isometrically represented on an $L^p$-space, for $p\neq 2$, 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.

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