ωℒ{\omega }_{{\mathcal{ {\mathcal L} }}}-biprojective and ω¯\overline{\omega }-contractible Banach algebras

Abstract

For a given Banach algebra ℳ{\mathcal{ {\mathcal M} }} and a continuous endomorphism ω\omega on ℳ{\mathcal{ {\mathcal M} }}, we define ℳ{\mathcal{ {\mathcal M} }} to be ωℒ{\omega }_{{\mathcal{ {\mathcal L} }}}-biprojective and ω¯\overline{\omega }-contractible. We then explore the relationship between them. Additionally, we show that l1(N∨){l}^{1}\left({{\mathbb{N}}}_{\vee }) is a ωℒ{\omega }_{{\mathcal{ {\mathcal L} }}}-biprojective Banach algebra. Finally, we examine the concept of ω\omega -pseudo amenability and ω\omega -approximate biprojectivity in Banach algebras. We demonstrate that for every unital Banach algebra ℳ{\mathcal{ {\mathcal M} }}, ω\omega -approximate biprojectivity and ω\omega -pseudo contractibility coincide.

Keywords

• banach algebra
• ωℒ-biprojective
• ω-contractible
• 43a20
• 46h25
• 47b47