Functional Analysis: Entering Hilbert Space

See our review of the first edition. The author has “expanded the material on normed vector spaces and their operators presented in Chapter 1 to include proofs of the Open Mapping Theorem, the Closed Graph Theorem and the Hahn-Banach Theorem.” Chapter six, on Fredholm theory in general Banach spaces, is also new in this edition. The approach to defining \(L^p\) spaces is unchanged from that of the first edition.

In the preface to the second edition, the author expresses the hope that the book can “serve as a general introduction to functional analysis viewed as a theory of infinite dimensional linear spaces and linear operators acting on them.” The book seems accessible to (well motivated) advanced undergraduates.

Fernando Q. Gouvêa is the editor of MAA Reviews.