A Short Course On Banach Space Theory

E-Book Overview

This short course on classical Banach space theory is a natural follow-up to a first course on functional analysis. The topics covered have proven useful in many contemporary research arenas, such as harmonic analysis, the theory of frames and wavelets, signal processing, economics, and physics. The book is intended for use in an advanced topics course or seminar, or for independent study. It offers a more user-friendly introduction than can be found in the existing literature and includes references to expository articles and suggestions for further reading.

E-Book Content

This page intentionally left blank A SHORT COURSE ON BANACH SPACE THEORY LONDON MATHEMATICAL SOCIETY STUDENT TEXTS Managing editor: Professor J. W. Bruce, Department of Mathematics, University of Hull, UK 3 4 5 7 8 9 11 12 13 15 17 18 19 20 21 22 23 24 25 26 27 28 29 31 32 33 34 35 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 Local fields, J.W.S. CASSELS An introduction to twistor theory: Second edition, S.A. HUGGETT & K.P. TOD Introduction to general relativity, L.P. HUGHSTON & K.P. TOD The theory of evolution and dynamical systems, J. HOFBAUER & K. SIGMUND Summing and nuclear norms in Banach space theory, G.J.O. JAMESON Automorphisms of surfaces after Nielsen and Thurston, A. CASSON & S. BLEILER Spacetime and singularities, G. NABER Undergraduate algebraic geometry, MILES REID An introduction to Hankel operators, J.R. PARTINGTON Presentations of groups: Second edition, D.L. JOHNSON Aspects of quantum field theory in curved spacetime, S.A. FULLING Braids and coverings: selected topics, VAGN LUNDSGAARD HANSEN Steps in commutative algebra, R.Y. SHARP Communication theory, C.M. GOLDIE & R.G.E. PINCH Representations of finite groups of Lie type, FRANC ¸ OIS DIGNE & JEAN MICHEL Designs, graphs, codes, and their links, P.J. CAMERON & J.H. VAN LINT Complex algebraic curves, FRANCES KIRWAN Lectures on elliptic curves, J.W.S. CASSELS Hyperbolic geometry, BIRGER IVERSEN An introduction to the theory of L-functions and Eisenstein series, H. HIDA Hilbert Space: compact operators and the trace theorem, J.R. RETHERFORD Potential theory in the complex plane, T. RANSFORD Undergraduate commutative algebra, M. REID The Laplacian on a Riemannian manifold, S. ROSENBERG Lectures on Lie groups and Lie algebras, R. CARTER, G. SEGAL, & I. MACDONALD A primer of algebraic D-modules, S.C. COUTINHO Complex algebraic surfaces, A. BEAUVILLE Young tableaux, W. FULTON A mathematical introduction to wavelets, P. WOJTASZCZYK Harmonic maps, loop groups, and integrable systems, M. GUEST Set theory for the working mathematician, K. CIESIELSKI Ergodic theory and dynamical systems, M. POLLICOTT & M. YURI The algorithmic resolution of diophantine equations, N.P. SMART Equilibrium states in ergodic theory, G. KELLER Fourier analysis on finite groups and applications, AUDREY TERRAS Classical invariant theory, PETER J. OLVER Permutation groups, P.J. CAMERON Riemann surfaces: A Primer, A. BEARDON Intoductory lectures on rings and modules, J. BEACHY ´ P. HAMBURGER, & A. MATE Set theory, A. HAJNAL, K-theory for C∗ -algebras, M. RORDAM, F. LARSEN, & N. LAUSTSEN A brief guide to algebraic number theory, H.P.F. SWINNERTON-DYER Steps in commutative algebra, R.Y. SHARP Finite Markov chains and algorithmic applications, O. HAGGSTROM The prime number theorem, G.J.O. JAMESON Topics in graph automorphisms and reconstruction, J. LAURI & R. SCAPELLATO Elementary number theory, group theory, and Ramanujan graphs, G. DAVIDOFF, P. SARNAK, & A. VALETTE A SHORT COURSE ON BANACH SPACE THEORY N. L. CAROTHERS Bowling Green State University    Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo Cambridge University Press The Edinburgh Building, Cambridge  , UK Published in the United States of America by Cambridge Universit
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