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On Arens-Michael algebras which do not have non-zero injective ⨶-modules

A. Pirkovskii (1999)

Studia Mathematica

A certain class of Arens-Michael algebras having no non-zero injective topological ⨶-modules is introduced. This class is rather wide and contains, in particular, algebras of holomorphic functions on polydomains in ℂ n , algebras of smooth functions on domains in ℝ n , algebras of formal power series, and, more generally, any nuclear Fréchet-Arens-Michael algebra which has a free bimodule Koszul resolution.

On left ϕ -biflat Banach algebras

Amir Sahami, Mehdi Rostami, Abdolrasoul Pourabbas (2020)

Commentationes Mathematicae Universitatis Carolinae

We study the notion of left ϕ -biflatness for Segal algebras and semigroup algebras. We show that the Segal algebra S ( G ) is left ϕ -biflat if and only if G is amenable. Also we characterize left ϕ -biflatness of semigroup algebra l 1 ( S ) in terms of biflatness, when S is a Clifford semigroup.

On the projectivity and flatness of some group modules

Gerhard Racher (2010)

Banach Center Publications

In the sequel of the work of H. G. Dales and M. E. Polyakov we give a few more examples of modules over the Banach algebra L¹(G) whose projectivity resp. flatness implies the compactness resp. amenability of the locally compact group G.

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