Introduction to Hilbert Space (New edition) by Sterling K. Berberian, ISBN 9780821819128

Publisher Description:
From the Preface: "This textbook has evolved from a set of lecture notes...In both the course and the book, I have in mind first- or second-year graduate students in Mathematics and related fields such as Physics...It is necessary for the reader to have a foundation in advanced calculus which includes familiarity with: least upper bound (LUB) and greatest lower bound (GLB), the concept of function, $\epsilon$'s and their companion $\delta$'s, and basic properties of sequences of real and complex numbers (convergence, Cauchy's criterion, the Weierstrass-Bolzano theorem). It is not presupposed that the reader is acquainted with vector spaces..., matrices..., or determinants...There are over four hundred exercises, most of them easy...It is my hope that this book, aside from being an exposition of certain basic material on Hilbert space, may also serve as an introduction to other areas of functional analysis."