Uniformly approaches projective and injective Banach modules

Abstract

The characteristics of projective and injective modules are evaluated. In addition, Ghahramani and Loy's view is extended to the Banach Modules. We indicate that the projective and injective Banach Modules can be characterized in the approximated concept. As a result, we approximately characterize the amenable, bi-projective, and bi-flat Banach algebras. In particular, we indicate that each of approximate uniform amenable algebra is amenable. In addition, we represent a new proof of the theorem, which has been expressed by Ghahramani and Loy for the approximate uniform contractibility [3]. Finally, we indicate that the proof result 3.4 [6] for the following article is incorrect; and we present a correct proof for it. We also extend this result.