Introduction to Banach Space Theory

Author: R.E. Megginson
Publisher:
Publication Date: 2003-06-01
Features: Since the study of normed spaces for their own sake evolved rather than arose fully formed, there is some room to disagree about who founded the field. Albert Bennett came close to giving the definition of a normed space in a 1916 paper [23] on an extension of Newton's method for finding roots, and in 1918, Frederic Riesz [195] based a generalization of the Fredholm theory of integral equations on the defining axioms of a complete normed space, though he did not use these axioms to study the general theory of such spaces. According to Jean Dieudonné [64], Riesz had at this time considered developing a general theory of complete normed spaces but never published anything in this direction. In a paper that appeared in 1921, Eduard Helly [102] proved what is now called Helly's theorem for bounded linear functionals. Along the way, he developed some of the general theory of normed spaces, but only in the context of norms on subspaces of the vector space of all sequences of complex scalars. This book is in English. Introduction to Banach Space Theory is an English introduction to Banach space theory.