Conway J.B. A Course in Functional Analysis (Graduate Texts in Mathematics)

Springer, 2nd edition, 1997. — 400 pages.An introductory text in functional analysis, aimed at the graduate student with a firm background in integration and measure theory. Unlike many modern treatments, this book begins with the particular and works its way to the more general, helping the student to develop an intuitive feel for the subject. For example, the author introduces the concept of a Banach space only after having introduced Hilbert spaces, and discussing their properties. The student will also apprecialte the large number of examples and exercises which have been included.