ABSTRACT
Cohen proved that any Banach algebra, with a bounded left approximate identity, admits the factorization property. Thereafter, the problems of bounded approximate identities and the factorization properties in Banach algebras have attracted a number of mathematicians. In this chapter, the authors wish to study the relationships among various bounded approximate identitites in Banach algebras. A commutative normed algebra with bounded point-wise weak approximate identity has a weak approximate identity (possibly unbounded). There is a long and interesting history for the non-factorization property of Segal algebras. Rudin’s methods can not extend to the case of arbitrary groups because they depend upon the use of the Fourier transform and particular functions in Euclidean n-space.
