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Functional Analysis: Entering Hilbert Space

Vagn Lundsgaard Hansen
Publisher: 
World Scientific
Publication Date: 
2016
Number of Pages: 
176
Format: 
Hardcover
Edition: 
2
Price: 
58.00
ISBN: 
9789814733922
Category: 
Textbook
[Reviewed by
Fernando Q. Gouvêa
, on
01/29/2016
]

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.

  • Basic Elements of Metric Topology
  • New Types of Function Spaces
  • Theory of Hilbert Spaces
  • Operators on Hilbert Spaces
  • Spectral Theory
  • Fredholm Theory
  • Exercises

Dummy View - NOT TO BE DELETED