Functional Analysis

Normed
vector spaces. Banach spaces. Quotient space. Linear operators and their adjoints. Hahn-Banach theorem. Uniform boundedness theorem. Closed graph theorem. Open mapping theorem. Weak topology. Banach-Alaoglu theorem. Reflexive spaces. Hilbert spaces. Ortonormal sets. Riesz’ representation theorem. Compact operators. Spectral theory of self-adjoint compact operators.

Referências:
BACHMAN, G., NARICI, L. – Functional Analysis. New York, Academic Press, 1966.
DUNFORD, N., SCHWARTZ, J. – Linear Operators, Vol. 1, Wiley Interscience Press, 1966.
REED, M., SIMON, B. – Methods of Modern Mathematical. Physics, Vol.1.  New York, Academic Press, 1972.
RIESZ, F., NAGY, B. – Functional Analysis. New York, Frederick Ungar, 1955.
RUDIN, WALTER (1-WI), Internat. Ser. Pure Appl. Math. McGraw-Hill, Inc., New York, 1991. xviii+424 pp. ISBN:0-07-054236-8

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