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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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