Krantz S.G. A Guide to Functional Analysis

Mathematical Association of America, 2013. — 150 pages. ISBN10: 0883853574Functional analysis is an abstract and powerful modern theory that occupies a central role in mathematics. This book provides a quick but precise introduction to the subject, covering everything that a beginning graduate student needs to know. The subject has its roots in the theory of infinite-dimensional vector spaces which is where the book begins, with preliminaries from the theory of normed linear spaces, Hilbert spaces, operator algebras and distributions. The reader will then encounter more advanced topics such as spectral theory, convexity and fixed-point theorems. It contains plenty of examples and exercises, making it an ideal basis for advanced undergraduate and graduate level courses in a subject that has become an essential part of every analyst's toolkit.Fundamentals
Ode to the dual space
Hilbert space
The algebra of operators
Banach algebra basics
Topological vector spaces
Distributions
Spectral theory
Convexity
Fixed-point theorems
Table of notation