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An Invitation to Operator Theory (Graduate Studies in Mathematics, V. 50)
Publisher: American Mathematical Society | Pages: 530 | 2002-09-10 | ISBN: 0821821466 | DJVU | 6 MB
An Invitation to Operator Theory (Graduate Studies in Mathematics, V. 50)
Publisher: American Mathematical Society | Pages: 530 | 2002-09-10 | ISBN: 0821821466 | DJVU | 6 MB
Product Description:
This book offers a comprehensive and reader-friendly exposition of the theory of linear operators on Banach spaces and Banach lattices using their topological and order structures and properties. Abramovich and Aliprantis give a unique presentation that includes many new and very recent developments in operator theory and also draws together results which are spread over the vast literature. For instance, invariant subspaces of positive operators and the Daugavet equation are presented in monograph form for the first time.
The authors keep the discussion self-contained and use exercises to achieve this goal. The book contains over 600 exercises to help students master the material developed in the text. The exercises are of varying degrees of difficulty and play an important and useful role in the exposition. They help to free the proofs of the main results of some technical details but provide students with accurate and complete accounts of how such details ought to be worked out. The exercises also contain a considerable amount of additional material that includes many well-known results whose proofs are not readily available elsewhere.
The companion volume, Problems in Operator Theory, also by Abramovich and Aliprantis, is available from the AMS as Volume 51 in the Graduate Studies in Mathematics series, and it contains complete solutions to all exercises in An Invitation to Operator Theory.
The solutions demonstrate explicitly technical details in the proofs of many results in operator theory, providing the reader with rigorous and complete accounts of such details. Finally, the book offers a considerable amount of additional material and further developments. By adding extra material to many exercises, the authors have managed to keep the presentation as self-contained as possible. The best way of learning mathematics is by doing mathematics, and the book Problems in Operator Theory will help achieve this goal.
Prerequisites to each book are the standard introductory graduate courses in real analysis, general topology, measure theory, and functional analysis. An Invitation to Operator Theory is suitable for graduate or advanced courses in operator theory, real analysis, integration theory, measure theory, function theory, and functional analysis. Problems in Operator Theory is a very useful supplementary text in the above areas. Both books will be of great interest to researchers and students in mathematics, as well as in physics, economics, finance, engineering, and other related areas, and will make an indispensable reference tool.
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Unbounded Linear Operators: Theory and Applications
Publisher: Dover Publications | Pages 208 | 2006-08-04 | ISBN 0486453316 | DJVU | 2.5 MB
Unbounded Linear Operators: Theory and Applications
Publisher: Dover Publications | Pages 208 | 2006-08-04 | ISBN 0486453316 | DJVU | 2.5 MB
Summary: Excellent complement to usual operator theory texts
Rating: 5
Most texts on functional analysis (linear operator theory) deal almost exclusively with bounded, or continuous, operators. However, when one studies some problems on differential equations one needs to work with unbounded operators.
This book constitutes a good starting point to get acquainted with such operators, mostly with closed and strictly singular ones. It includes some applications to perturbation theory and ordinary differential equations, and gives some comments on the Dirichlet problem for PDE's. Finally, its extensive list of references motivates you to deeper study.
Israel Gohberg, Seymour Goldberg
“Basic Operator Theory"
Birkhauser | 1981-03 | ISBN: 3764330287 | 285 pages | Djvu | 2,9 MB
Basic Operator Theory provides an introduction to functional analysis with an emphasis on the theory of linear operators and its application to differential and integral equations, approximation theory, and numerical analysis. A textbook designed for senior undergraduate and graduate students, Basic Operator Theory begins with the geometry of Hilbert space and proceeds to the spectral theory for compact self-adjoint operators with a wide range of applications. Part of the volume is devoted to Banach spaces and operators acting on these spaces. Presented as a natural continuation of linear algebra, Basic Operator Theory provides a firm foundation in operator theory, an essential part of mathematical training for students of mathematics, engineering, and other technical sciences.
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A. Ya. Helemskii
“Lectures And Exercises on Functional Analysis"
American Mathematical Society | 2006-08-22 | ISBN: 0821840983 | 468 pages | Djvu | 3,1 Mb
The book is based on courses taught by the author at Moscow State University. Compared to many other books on the subject, it is unique in that the exposition is based on extensive use of the language and elementary constructions of category theory. Among topics featured in the book are the theory of Banach and Hilbert tensor products, the theory of distributions and weak topologies, and Borel operator calculus. The book contains many examples illustrating the general theory presented, as well as multiple exercises that help the reader to learn the subject. It can be used as a textbook on selected topics of functional analysis and operator theory. Prerequisites include linear algebra, elements of real analysis, and elements of the theory of metric spaces.
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E. B. Davies
Spectral Theory and Differential Operators
Cambridge University Press | ISBN: 0521472504 | 1995 | 192 pages | djvu | 1.4 MB
In this book, Davies introduces the reader to the theory of partial differential operators, up to the spectral theorem for bounded linear operators on Banach spaces. He also describes the theory of Fourier transforms and distributions as far as is needed to analyze the spectrum of any constant coefficient partial differential operator. He also presents a completely new proof of the spectral theorem for unbounded self-adjoint operators and demonstrates its application to a variety of second order elliptic differential operators. Finally, the book contains a detailed account of the application of variational methods to estimate the eigenvalues of operators with measurable coefficients defined by the use of quadratic form techniques. Illustrated with many examples, it is well-suited to graduate-level work.
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Recent Advances in Operator Theory and Its Applications: The Israel Gohberg Anniversary Volume
Publisher: Birkhauser | 2005-10 | ISBN 3764372907 | Pages: 478 | PDF | 4 MB
This book contains a selection of carefully refereed research papers, most of which were presented at the 14th International Workshop on Operator Theory and its Applications (IWOTA) held at Cagliari, Italy (June 24-27, 2003). The papers, many of which have been written by leading experts in the field, concern a wide variety of topics in modern operator theory and applications, with emphasis on differential operators and numerical methods. Included are papers on the structure of operators, spectral theory of differential operators, theory of pseudo-differential operators and Fourier integral operators, numerical methods for solving nonlinear integral equations, singular integral equations, and Toeplitz systems. Other main topics covered are inverse problems for canonical systems, factorization methods, metric constrained interpolation, mathematical system theory, and elements of multivariable operator theory. The book will be of interest to a wide audience of pure and applied mathematicians and engineers.
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