If a Banach algebra A is neither Arens regular nor commutative, under what conditions there exists m in A** such that m\Box m \neq m\diamond m?

16 July 2021 1 3K Report

A** is the bidual of A equipped with Arens products.

Lav Singh

No I do not have such an example. Indeed I am trying to prove that if A is neither Arens regular nor commutative, then there exists m in A** such that $m\box m$ is not equal to $m\diamond m$.

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