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Paper IPM / M / 15556  


Abstract:  
In this paper, we study the existence of left and right approximate iden
tities of â 1 Munn algebras. We introduce a concept of virtual invertibility as a general
ization of invertibility for a matrix. Then we show that having left and right approximate
identities of a Munn algebra implies that the related sandwich matrix is virtually invert
ible. As an application, we investigate approximate amenability over Munn algebras. We
present some necessary conditions for the approximate amenability of Munn algebras
in a general case. Finally, we apply the results to study the approximate amenability
of Rees matrix semigroup algebras.
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