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Elements of functional analysis

Elements of functional analysis
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Field name Details
Dewey Class 515.7 (DDC 19)
Title Elements of functional analysis
(M)
/ I.J. Meddox
Author Maddox, Ivor John , 1936-
Edition statement 2nd ed.
Publication Cambridge : Cambridge University Press , c1988
Physical Details xii, 242 pages ; 23 cm.
ISBN 0-521-35350-5
Summary Note Preface to the second edition; Preface to the first edition; Part I. Basic Set Theory and Analysis: 1. Sets and functions; 2. Real and complex numbers; 3. Sequences of functions, continuity, differentiability; 4. Inequalities; Part II. Metric and Topological Spaces: 1. Metric and semimetric spaces; 2. Complete metric spaces; 3. Some metric and topological concepts; 4. Continuous functions on metric and topological spaces; 5. Compact sets; 6. Category and uniform boundedness; Part III. Linear and Linear Metric Spaces: 1. Linear spaces; 2. Subspaces, dimensionality, factorspaces, convex sets; 3. Metric linear spaces, topological linear spaces; 4. Basis; Part IV. Normed Linear Spaces: 1. Convergence and completeness; 2. Linear operators and functionals; 3. The Banach-Steinhaus theorem; 4. The open mapping and closed graph theorems; 5. The Hahn-Banach extension; 6. Weak topology and weak convergence; Part V. 1. Algebras and Banach algebras; 2. Homomorphisms and isomorphisms; 3. The spectrum and the Gelfand-Mazaur theorem; 4. The Weiner algebra; Part VI. Hilbert Space: 1. Inner product and Hilbert spaces; 2. Orthonormal sets; 3. The dual space of a Hilbert space; 4. Symmetric and compact operators; Part VII. Applications: 1. Differential and integral problems; 2. The Sturm-Liouville problem; 3. Matrix transformations in sequence spaces; Appendix; Bibliography; Index.:
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