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This title in other editionsThe Elements of Operator Theoryby Carlos Kubrusly
Synopses & ReviewsPublisher Comments:"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 wellorganized 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 userfriendly, motivating style, it covers the fundamental topics of the field in a systematic fashion while avoiding a formulacalculation 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 selfcontained textbook, The Elements of Operator Theory, Second Edition is an excellent resource for the classroom as well as a selfstudy reference for researchers. Prerequisites comprise an introduction to analysis and basic experience with functions of a complex variable, which most firstyear 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.
Synopsis:This second edition is a conceptdriven book that includes a significant expansion of the problems and solutions used to illustrate the principles of operator theory. Written in a userfriendly style, it presents fundamental topics in a systematic fashion.
Synopsis:This second edition of Elements of Operator Theory is a conceptdriven textbook
About the AuthorCarlos Kubrusly's research deals with Hilbertspace 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.
Table of ContentsPreface * Set Theoretic Structures * Algebraic Structures * Topological Structures * Banach Spaces * Hilbert Spaces * The Spectral Theorem * References * Index
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Related SubjectsScience and Mathematics » Mathematics » Algebra » General Science and Mathematics » Mathematics » Applied Science and Mathematics » Mathematics » Functional Analysis Science and Mathematics » Mathematics » General Science and Mathematics » Mathematics » Operator Analysis 

