On a Notion of Biflatness Related to a Closed Ideal

Abstract

This study is motivated through the so‐called approximate homology results of Banach algebras arising from their closed ideals. For a Banach algebra , the notion of approximate ‐biflatness is presented, where is a closed ideal of . Moreover, some related results between our concept of homology and the known notions of amenability in the setting of Banach algebras are studied. For a locally compact group G, a necessary and sufficient condition for the measure algebra M(G) to be approximately L1(G)‐biflat is found, where L1(G) is the correspondence group algebra of G. Additionally, some applications of (approximately) ‐biflatness for the Fourier algebras, Lipschitz algebras, and matrix algebras are given. Furthermore, for validation of our concept, some examples for the differences between this new notion and the classical ones are indicated.