σ-Biflat Banach Algebras; the Older and the New Notions

摘要

We introduce a new concept of sigma-biflatness for Banach algebras. We show difference between this new concept and the classical one. A characterization of sigma-biflatness is also given. As we shall see, sigma-biflatness is closely related to the notions of sigma-amenability and sigma-biprojectivity. We compare our definition with the existing notion of sigma-biflat Banach algebras in the sense of Ghorbani and Bami (Bull Iran Math Soc 39(3):507-515, 2013). In addition, sigma-biflatness of tensor product of Banach algebras is discussed.