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Principles of Functional Analysis
Martin Schechter
Price
1330.00
ISBN
9780821848562
Language
English
Pages
448
Format
Paperback
Dimensions
180 x 240 mm
Year of Publishing
2009
Territorial Rights
Restricted
Imprint
American Mathematical Society

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Functional analysis plays a crucial role in the applied sciences as well as in mathematics. It is a beautiful subject that can be motivated and studied for its own sake. In keeping with this basic philosophy, the author has made this introductory text accessible to a wide spectrum of students, including beginning-level graduates and advanced undergraduates.

The exposition is inviting, following threads of ideas, describing each as fully as possible, before moving on to a new topic. Supporting material is introduced as appropriate, and only to the degree needed. Some topics are treated more than once, according to the different contexts in which they arise.

The prerequisites are minimal, requiring little more than advanced calculus and no measure theory. The text focuses on normed vector spaces and their important examples, Banach spaces and Hilbert spaces. The author also includes topics not usually found in texts on the subject.

This Second Edition incorporates many new developments while not overshadowing the book's original flavor. Areas in the book that demonstrate its unique character have been strengthened. In particular, new material concerning Fredholm and semi-Fredholm operators is introduced, requiring minimal effort as the necessary machinery was already in place. Several new topics are presented, but relate to only those concepts and methods emanating from other parts of the book. These topics include perturbation classes, measures of noncompactness, strictly singular operators, and operator constants.

Overall, the presentation has been refined, clarified, and simplified, and many new problems have been added.

Martin Schechter, University of California, Irvine, CA
  • Basic notions
  • Duality
  • Linear operators
  • The Riesz theory for compact operators
  • Fredholm operators
  • Spectral theory
  • Unbounded operators
  • Reflexive Banach spaces
  • Banach algebras
  • Semigroups
  • Hilbert space
  • Bilinear forms
  • Selfadjoint operators
  • Measures of operators
  • Examples and applications
  • Glossary
  • Major Theorems
  • Bibliography
  • Index
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