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Principles of Functional Analysis
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Principles of Functional Analysis

Principles of Functional Analysis

Martin Schechter

424 pages, parution le 22/01/2002

Résumé

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.

Contents

  • 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
  • Bibliography
  • Index

Caractéristiques techniques

  PAPIER
Éditeur(s) American Mathematical Society (AMS)
Auteur(s) Martin Schechter
Parution 22/01/2002
Nb. de pages 424
Format 18 x 26
Couverture Relié
Poids 950g
Intérieur Noir et Blanc
EAN13 9780821828953
ISBN13 978-0-8218-2895-3

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