Categorical bases in Banach spaces

Abstract

The primary purpose of this paper is to study the relationships between categorical bases and classical (Schauder) bases in Banach spaces. Several types of categorical bases are investigated in categories of Hausdorff linear topological spaces and continuous linear functions. Several characterizations of categorical bases are derived in the category of all Banach spaces and continuous linear maps, and an isomorphism theorem is obtained which guarantees preservation of certain types of categorical bases under equivalences.