Elementary Functional Analysis

This book is meant as a text for a first-year graduate course in analysis. In a sense, it covers the same topics as elementary calculus but treats them in a manner suitable for people who will be using it in further mathematical investigations.

In July of 1996, the conference Nonlinear Analysis and its Applications in Engineering and Economics took place on the Greek island of Samos, the birthplace of Pythagoras.

In this set of lecture notes, we present a culmination of results on infinite matrices which were evolved by the members of the Katowice Br-anch of the Mathematics Institute of the Polish Academy of Sciences. In the early history of functional analysis Hsliding humpH methods were used extensively to establish some of the early abstract results in functional analysis. For example, the first proofs of versions of the Uniform Boundedness Principle by Hahn and Banach and Hildebrand utilized sliding hump methods ([18], [39], [42], [35]).