The structure and amenability of \(\ell^P\)-Munn algebras (Q553424)

In the present paper the authors introduce the notion of \({\mathcal {LM}}^p_I({\mathcal A})\), where \({\mathcal A}\) is a Banach space, \(I\) is an index set and \(1 \leq p<\infty\). They find necessary and sufficient conditions for \({\mathcal {LM}}^p_I({\mathcal A})\) to be a Banach algebra, and investigate the amenability of this Banach algebra. Applications to \(\ell^p (S)\) \((1 \leq p<\infty)\), where \(S\) is a Brandt semigroup, are also given.