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ISBN: 9780521603720 9780521842839 0521603722 0521842832 9780511614057 0511080476 9780511080470 0511614055 9780511079719 0511079710 1107140501 051120650X 0511567502 Year: 2005 Publisher: Cambridge : Cambridge University Press,
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This is a short course on Banach space theory with special emphasis on certain aspects of the classical theory. In particular, the course focuses on three major topics: the elementary theory of Schauder bases, an introduction to Lp spaces, and an introduction to C(K) spaces. While these topics can be traced back to Banach himself, our primary interest is in the postwar renaissance of Banach space theory brought about by James, Lindenstrauss, Mazur, Namioka, Pelczynski, and others. Their elegant and insightful results are useful in many contemporary research endeavors and deserve greater publicity. By way of prerequisites, the reader will need an elementary understanding of functional analysis and at least a passing familiarity with abstract measure theory. An introductory course in topology would also be helpful; however, the text includes a brief appendix on the topology needed for the course.
Banach spaces. --- Banach, Espaces de --- Functions of complex variables --- Generalized spaces --- Topology
ISBN: 9780511814228 1316087204 1139635980 1139648713 1139638262 1139641107 0511814224 9780521497497 9780521497565 9781139648714 9781139638265 9781139641104 0521497493 0521497566 Year: 2000 Publisher: Cambridge : Cambridge University Press,
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This is a course in real analysis directed at advanced undergraduates and beginning graduate students in mathematics and related fields. Presupposing only a modest background in real analysis or advanced calculus, the book offers something to specialists and non-specialists. The course consists of three major topics: metric and normed linear spaces, function spaces, and Lebesgue measure and integration on the line. In an informal style, the author gives motivation and overview of new ideas, while supplying full details and proofs. He includes historical commentary, recommends articles for specialists and non-specialists, and provides exercises and suggestions for further study. This text for a first graduate course in real analysis was written to accommodate the heterogeneous audiences found at the masters level: students interested in pure and applied mathematics, statistics, education, engineering, and economics.
Mathematical analysis. --- 517.1 Mathematical analysis --- Mathematical analysis --- 517.1 --- 517.51 --- integralen --- Lebesgue --- wiskunde --- 517.51 Functions of a real variable. Real functions --- Functions of a real variable. Real functions --- analyse
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