Principles of Functional Analysis

Martin Schechter

424 pages, parution le 22/01/2002

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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