00000cmm a22000004a 4500 UP-99796217611212558 Buklod 20230215085534.0 m go j cr |n |||auu|a 110228s2011 xxu u eng d 9780817649982 (eBook) 0817649980 (eBook) (iLib)UPD-00215704361 DML eng DMLUC QA 329 K83 2011eb Kubrusly, Carlos S. 1947- The elements of operator theory [electronic resource] Carlos S. Kubrusly. 2nd ed. Boston New York Birkhäuser Springer c2011. 1 online resource (xv, 539 p.) Preface -- Set Theoretic Structures -- Algebraic Structures -- Topological Structures -- Banach Spaces -- Hilbert Spaces -- The Spectral Theorem -- References -- Index. IP-based subscription, access limited to within on-campus computer network. Access via Electronic Resources of the UPD University Library Website. "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. Electronic reproduction. New York SpringerLink c2011. Available via World Wide Web through SpringerLink. Operator theory. Electronic books. SpringerLink (Online service). Electronic Resource Available for University of the Philippines Diliman via SpringerLink. Click here to access http://dx.doi.org/10.1007/978-0-8176-4998-2 FO Monograph UPD DMLR Electronic Resource