The structure of Jordan contractible Banach algebras

Abstract

In this paper, we define the Jordan notions of contractibility and biprojectivity of Banach algebras and comparing to the classical notions of contractibility and biprojectivity. Also, we introduce the notion of Jordan diagonal and find relations between these Jordan notions. As a main result, we show that the Banach algebra [Formula: see text] is unital and Jordan contractible if and only if it has a Jordan diagonal if and only if [Formula: see text] is unital and Jordan biprojective, whenever [Formula: see text] is a Banach [Formula: see text]-bimodule.