Solved and unsolved problems in generalized notions of amenability for Banach algebras

TL;DR

This paper surveys recent advances and core problems in generalized notions of amenability for Banach algebras, including approximate and pseudo-amenability, highlighting their significance and presenting new results.

Contribution

It provides a comprehensive overview of recent research on generalized amenability in Banach algebras and introduces new findings in the area.

Findings

Discussion of core problems in generalized amenability

Insights into the significance of solutions for the field

Presentation of new results in the area

Abstract

We survey the recent investigations on (bounded, sequential) approximate amenability/contractibility and pseudo-amenability/contractibility for Banach algebras. We will discuss the core problems concerning these notions and address the significance of any solutions to them to the development of the field. A few new results are also included.