Banach function algebras generated by normed vector spaces and linear functionals

Given a non-zero normed vector space A and a contractive non-zero element φ 2 A (the dual space of A), we introduce the Banach function algebra Cφ(K), where K = B(0)1 is the closed unit ball of A. We investigate and characterize some basic properties, such as idempotent elements, nilpotent elements and bounded approximate identities of the Banach function algebra Cφ(K). Finally we characterize some elements of the character space △(Cφ(K)).

کلیدواژه ها:

Banach function algebra ، Normed vector space ، Bounded approximate identity ، Idempotent element ، Character space.