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Paper   IPM / M / 15556
School of Mathematics
  Title:   Approximate identities of L1 -Munn algebras and applications to semigroup algebras
  Author(s):  Maedeh Soroushmehr
  Status:   To Appear
  Journal: Publ. Math. Debrecen
  Supported by:  IPM
In this paper, we study the existence of left and right approximate iden- tities of ‘ 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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