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Functional analysis and applications (book list)

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This is a section of the Basic Math Library List


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 9. Functional analysis and applications 
    Operator algebras. Non-commutative geometry, spectra of random matrices. K-theory of C*-algebras,
    structure of factors and their automorphism groups, operator-algebraic aspects of quantum field theory,
    linear and non-linear functional analysis, geometry of Banach spaces, Asymptotic geometric analysis.
    Connections to ergodic theory. 
    Connections with sections 5, 6, 7, 8, 10, 11, 12, 13.



Brezis, Haïm Analyse fonctionnelle. (French) [Functional analysis] Théorie et applications. [Theory and applications] Masson, Paris, 1983. xiv+234 pp. 125 F. ISBN 2-225-77198-7 => (Persian translation in 2 vol's by B. Djafari Rouhani)


Rudin, Functional Analysis


Reed, Michael; Simon, Barry Methods of modern mathematical physics. II. Fourier analysis, self-adjointness. Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1975. xv+361 pp.


Reed, Michael; Simon, Barry Methods of modern mathematical physics. I. Functional analysis. Academic Press, New York-London, 1972. xvii+325 pp.




Beauzamy, Bernard. Introduction to Banach Spaces and Their Geometry Amsterdam: North-Holland, 1982.

Berberian, Sterling K. Introduction to Hilbert Space, New York, NY: Chelsea, 1976. Second Edition.

Bollobas, Bela. Linear Analysis New York, NY: Cambridge University Press, 1990.

Bridges, Douglas S. Constructive Functional Analysis Brooklyn, NY: Pitman, 1979.

Dieudonne, Jean. Treatise on Analysis, New York, NY: Academic Press, 1969--88. 7 Vols.

  • Dunford, Nelson and Schwartz, Jacob T. Linear Operators, New York, NY: John Wiley, 1958, 1963. Parts I and II.

Flett, T.M. Differential Analysis: Differentiation, Differential Equations, and Differential Inequalities New York, NY: Cambridge University Press, 1980.

Gamelin, Theodore W. Uniform Algebras New York, NY: Chelsea, 1984.

  • Gel'fand, Israel M., et al. Generalized Functions, New York, NY: Academic Press, 1964--68. 5 Vols.
  • Gel'fand, Israel M.; Raikov, D.A.; and Shilov, G.E. Commutative Normed Rings New York, NY: Chelsea, 1964.

Goffman, Casper and Pedrick, George. A First Course in Functional Analysis, New York, NY: Chelsea, 1983. Second Edition.

Grothendieck, A. Topological Vector Spaces New York, NY: Gordon and Breach, 1973.

Halmos, Paul R. Introduction to Hilbert Space New York, NY: Chelsea, 1951.

Halmos, Paul R. A Hilbert Space Problem Book, New York, NY: Springer-Verlag, 1982. Second Edition.

  • Hille, Einar and Phillips, R.S. Functional Analysis and Semi-Groups Providence, RI: American Mathematical Society, 1957.
  • Hoffman, Kenneth. Banach Spaces of Analytic Functions Mineola, NY: Dover, 1980.

Kirillov, A.A. and Gvishiani, A.D. Theorems and Problems in Functional Analysis New York, NY: Springer-Verlag, 1982.

  • Liusternik, L. and Sobolev, V. Elements of Functional Analysis New York, NY: Frederick Ungar, 1961.

Lorch, Edgar R. Spectral Theory New York, NY: Oxford University Press, 1962.

Nachbin, Leopoldo. Introduction to Functional Analysis: Banach Spaces and Differential Calculus New York, NY: Marcel Dekker, 1981.

  • Naimark, M.A. Normed Rings Groningen: Wolters-Noordhoff, 1960.
    • Riesz, Frigyes and Nagy, Bela Sz. Functional Analysis Mineola, NY: Dover, 1990.
    • Rudin, Walter. Functional Analysis New York, NY: McGraw-Hill, 1973.
  • Taylor, Angus E. and Lay, David C. Introduction to Functional Analysis, New York, NY: John Wiley, 1958, 1980. Second Edition.
    • Yosida, Kosaku. Functional Analysis, New York, NY: Springer-Verlag, 1965, 1980. Sixth Edition.

Young, Nicholas. An Introduction to Hilbert Space New York, NY: Cambridge University Press, 1988.


Operator Theory

Arveson, William. An Invitation to $C^*$-Algebras New York, NY: Springer-Verlag, 1976.

    • Banach, Stefan. Theory of Linear Operators New York, NY: Elsevier Science, 1987.

Brown, Arlen and Pearcy, Carl. Introduction to Operator Theory I: Elements of Functional Analysis New York, NY: Springer-Verlag, 1977.

Gohberg, Israel and Goldberg, Seymour. Basic Operator Theory New York, NY: Birkhauser, 1981.

  • Kadison, Richard V. and Ringrose, John R. Fundamentals of the Theory of Operator Algebras, New York, NY: Academic Press, 1983. Vol. I: Elementary Theory.
  • Kato, Tosio. Perturbation Theory for Linear Operators, New York, NY: Springer-Verlag, 1976. Second Edition.



ISBN 0125850506 : Functional Analysis

ISBN 0125850042 : Methods of Modern Mathematical Physics

ISBN 0120903504 : Nonlinearity and functional analysis

ISBN 0387902031 : Theory of Functional Differential Equations

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