Verwandte Artikel zu Elements of Operator Theory
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Inhaltsangabe
{\it Elements of Operatory Theory} is aimed at graduate students as well as a new generation of mathematicians and scientists who need to apply operator theory to their field. Written in a user-friendly, motivating style, fundamental topics are presented in a systematic fashion, i.e., set theory, algebraic structures, topological structures, Banach spaces, Hilbert spaces, culminating with the Spectral Theorem, one of the landmarks in the theory of operators on Hilbert spaces. The exposition is concept-driven and as much as possible avoids the formula-computational approach. Key features of this largely self-contained work include: * required background material to each chapter * fully rigorous proofs, over 300 of them, are specially tailored to the presentation and some are new * more than 100 examples and, in several cases, interesting counterexamples that demonstrate the frontiers of an important theorem * over 300 problems, many with hints * both problems and examples underscore further auxiliary results and extensions of the main theory; in this non-traditional framework, the reader is challenged and has a chance to prove the principal theorems anew This work is an excellent text for the classroom as well as a self-study resource for researchers. Prerequisites include an introduction to analysis and to functions of a complex variable, which most first-year graduate students in mathematics, engineering, or another formal science have already acquired. Measure theory and integration theory are required only for the last section of the final chapter.
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Review
"The author endeavors to present the concepts and ideas as an alternative to the computational approach, trying to avoid long calculations by stressing the mathematical thoughts behind the statements. . . . many problems [are] stated throughout the book, very often accompanied by hints." —Mathematical Reviews "This is a rigorous, logically well-organized textbook presenting basic principles and elementary theory of operators. It is written with great care, gradually increasing in complexity. The forte features of the book are the teaching style, illuminating explanation of numerous delicate points, detailed presentation of topics. Hence, the book can be warmly recommended to a first work for the study of operator theory . . . it is an admirable work for a modern introduction in operator theory." —Zentralblatt Math
From the Back Cover
"The author endeavors to present the concepts and ideas as an alternative to the computational approach, trying to avoid long calculations by stressing the mathematical thoughts behind the statements. . . . many problems [are] stated throughout the book, very often accompanied by hints." —Mathematical Reviews (review of the first edition) "This is a rigorous, logically well-organized textbook presenting basic principles and elementary theory of operators. It is written with great care, gradually increasing in complexity. The forte features of the book are the teaching style, illuminating explanation of numerous delicate points, and detailed presentation of topics. Hence, the book can be warmly recommended to a first work for the study of operator theory . . . it is an admirable work for a modern introduction in operator theory." —Zentralblatt MATH (review of the first edition) This fully revised, updated, and corrected edition of The Elements of Operator Theory includes a significant expansion of problems and solutions used to illustrate the principles of operator theory. Written in a user-friendly, motivating style, it covers the fundamental topics of the field in a systematic fashion while avoiding a formula-calculation approach. The book maintains the logical and linear organization of the title’s first edition, progressing through set theory, algebraic structures, topological structures, Banach spaces, and Hilbert spaces before culminating in a discussion of the Spectral Theorem. Included in the presentation are * More than 300 rigorous proofs, specially tailored to the presentation. * Approximately 150 examples, and several interesting counterexamples that demonstrate the frontiers of an important theorem. * Over 300 problems, with many hints, and 20 pages of additional exercises for the second edition. Throughout, the pedagogical tone and the blend of examples and exercises encourage and challenge the reader to explore fresh approaches to theorems and auxiliary results. A self-contained textbook, The Elements of Operator Theory, Second Edition is an excellent resource for the classroom as well as a self-study reference for researchers. Prerequisites comprise an introduction to analysis and basic experience with functions of a complex variable, which most first-year graduate students in mathematics, engineering, or other formal sciences have already acquired. Measure theory and integration theory are necessary only for the last section of the final chapter.
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