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On convolution operators with small support which are far from being convolution by a bounded measure

Edmond Granirer (1994)

Colloquium Mathematicae

Let C V p ( F ) be the left convolution operators on L p ( G ) with support included in F and M p ( F ) denote those which are norm limits of convolution by bounded measures in M(F). Conditions on F are given which insure that C V p ( F ) , C V p ( F ) / M p ( F ) and C V p ( F ) / W are as big as they can be, namely have l as a quotient, where the ergodic space W contains, and at times is very big relative to M p ( F ) . Other subspaces of C V p ( F ) are considered. These improve results of Cowling and Fournier, Price and Edwards, Lust-Piquard, and others.

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.

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