Principles of functional analysis
著者
書誌事項
Principles of functional analysis
（Graduate studies in mathematics, v. 36）
American Mathematical Society, c2002
2nd ed
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注記
Bibliography: p. 419-421
Includes index
内容説明・目次
内容説明
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.
目次
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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