Basic Operator Theory
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Beschreibung
rii application of linear operators on a Hilbert space. We begin with a chapter on the geometry of Hilbert space and then proceed to the spectral theory of compact self adjoint operators; operational calculus is next presented as a nat ural outgrowth of the spectral theory. The second part of the text concentrates on Banach spaces and linear operators acting on these spaces. It includes, for example, the three 'basic principles of linear analysis and the Riesz Fredholm theory of compact operators. Both parts contain plenty of applications. All chapters deal exclusively with linear problems, except for the last chapter which is an introduction to the theory of nonlinear operators. In addition to the standard topics in functional anal ysis, we have presented relatively recent results which appear, for example, in Chapter VII. In general, in writ ing this book, the authors were strongly influenced by re cent developments in operator theory which affected the choice of topics, proofs and exercises. One of the main features of this book is the large number of new exercises chosen to expand the reader's com prehension of the material, and to train him or her in the use of it. In the beginning portion of the book we offer a large selection of computational exercises; later, the proportion of exercises dealing with theoretical questions increases. We have, however, omitted exercises after Chap ters V, VII and XII due to the specialized nature of the subject matter.
"Written by two distinguished specialists in both research and education, the book represents an excellent introduction to a subject of increasing power and importance in today's mathematics. It is designed for senior undergraduate and graduate students in mathematics, engineering, etc., but it should be welcome in the library of any person interested in operator theory and its applications." - F.-H. Vasilescu for AMS
"The text is self-contained as it is possible, and contains a large number of exercises. It is highly offered to graduate and senior undergraduate students in mathematics." -- L. Gehér for Acta Sci. Math. (Szeged)
Autor*in
Israel Gohberg
Themen in »Basic Operator Theory«
Applications of Mathematics Functional Analysis Operator Theory Banach space calculus equation function functional analysis geometry Hilbert space linear optimization mathematics operational calculus operator operator theory