Debnath L., Mikusinski P. Introduction to Hilbert Spaces with Applications

Academic Press, 1990. — 508 pages.Functional analysis is one of the central areas of modern mathematics, and the theory of Hilbert spaces is the core around which functional analysis has developed. Hilbert spaces have a rich geometric structure because they are endowed with an inner product which allows the introduction of the concept of orthogonality of vectors. We believe functional analysis is best approached through a sound knowledge of Hilbert space theory. Our belief led us to prepare an earlier manuscript which was used as class notes for courses on Hilbert space theory at the University of Central Florida and Georgia Institute of Technology. This book is essentially based on those notes.