Johnson pseudo-contractibility of second duals of certain Banach algebras

In this paper, we study Johnson pseudo-contractibility of second dual of some Banach algebras. We show that the semigroup algebra [Formula: see text] is Johnson pseudo-contractible if and only if [Formula: see text] is a finite amenable group, where [Formula: see text] is an archimedean semigroup. We also show that the matrix algebra [Formula: see text] is Johnson pseudo-contractible if and only if [Formula: see text] is finite. We study Johnson pseudo-contractibility of certain projective tensor product second duals Banach algebras.

Representing N-semigroups

An N-semigroup is a commutative, cancellative, archimedean semigroup with no idempotent element. This paper obtains a representation of finitely generated N-semigroups as the subdirect product of an abelian group and a subsemigroup of the additive positive integers.