Abstract

This article examines Stefan Banach’s contributions to the field of functional analysis based on the concept of structure and the multiply-flavored expression of generality that arises in his work on linear operations. More specifically, it discusses the two stages in the process by which Banach elaborated a new framework for functional analysis where structures were bound to play an essential role. It considers whether Banach spaces, or complete normed vector spaces, were born in Banach’s first paper, the 1922 doctoral dissertation On operations on abstract spaces and their application to integral equations. It also analyzes what appears to be the core of Banach’s 1922 article and the transformation into a general setting that it represents. The main achievements of Banach’s dissertation, as well as all the essential features that bear witness to the birth of a new theory, are concentrated in the study of linear operations.