Taylor A.E. Introduction to functional analysis

Wiley, 1958. — 438 p.
This book provides a carefully organized, readable, and unusually complete introduction to functional analysis. The central theme is the theory of normed linear spaces and operators between normed linear spaces. Where the property of completeness is crucial, Banach spaces are used. Special developments are given for Hubert space when results of a distinctive nature can be obtained. There are many problems. These are chosen carefully and make a significant contribution to the completeness of the book.