The Elements of Operator Theory - Hardcover

Kubrusly, Carlos S.

Hardcover

ISBN 10: 0817649972 ISBN 13: 9780817649975

Verlag: Birkhäuser, 2011

Inhaltsangabe

This second edition of Elements of Operator Theory is a concept-driven textbook that includes a significant expansion of the problems and solutions used to illustrate the principles of operator theory. Written in a user-friendly, motivating style intended to avoid the formula-computational approach, fundamental topics are presented in a systematic fashion, i.e., set theory, algebraic structures, topological structures, Banach spaces, and Hilbert spaces, culminating with the Spectral Theorem.

Included in this edition: more than 150 examples, with several interesting counterexamples that demonstrate the frontiers of important theorems, as many as 300 fully rigorous proofs, specially tailored to the presentation, 300 problems, many with hints, and an additional 20 pages of problems for the second edition.

*This self-contained work is an excellent text for the classroom as well as a self-study resource for researchers.

Über diesen Titel

Über die Autorin bzw. den Autor

Carlos Kubrusly's research deals with Hilbert-space operators, focusing on the Invariant Subspace Problem and its connection with the characterization of weakly and strongly stable operators. The author has published several books, including An Introduction to Models and Decompositions in Operator Theory, Elements of Operator Theory, Hilbert Space Operators: A Problem Solving Approach, and Measure Theory: A First Course.

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"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.

Details zur Ausgabe

• Verlag: Birkhäuser
• Erscheinungsdatum: 2011
• Sprache: Englisch
• ISBN 10: 0817649972
• ISBN 13: 9780817649975
• Einband: Tapa dura
• Anzahl der Seiten: 556
• Kontakt zum Hersteller: Nicht verfügbar
• Verantwortliche Person: Nicht verfügbar