Functional Analysis - I, 3 Cr. Hours,For students of B.S.Mathematics.
CHAPTER-1 :METRIC SPACES
1-Review of metric spaces
2-Convergence in metric spaces
3-Complete metric spaces
4-Completeness proofs
5-Dense sets
6-Separable spaces
7-Nowhere dense sets
8-Baire category theorem
CHAPTER-2: NORMED SPACES
1-Normed linear spaces
2-Banach spaces
3-Convex sets
4-Quotient spaces
5-Equivalent norms
6- Finite dimensional normed spaces
7-Linear operators
8-Continuous or bounded linear operators
9-Linear functionals
10-Dual spaces
CHAPTER-3: INNER PRODUCT SPACES
1-Definition and examples
2-Orthonormal sets and bases
3-Annihilators
4-Projections in Hilbert spaces
5-Linear functionals on Hilbert spaces
6-Reflexivity of Hilbert spaces

Recommended Books
1. E. Kreyszig, Introduction to Functional Analysis with Applications, (John Wiley and Sons,2004)
2. A. L. Brown and A. Page, Elements of Functional Analysis, (Van Nostrand Reinhold
London, 1970)
3. G. Bachman and L. Narici, Functional Analysis, (Academic Press, New York, 1966)
4. F. Riesz and B. Sz. Nagay, Functional Analysis, (Dover Publications, Inc., New York,Ungar, 1965)
5. A. E. Taylor, Functional Analysis, (John Wiley and Sons, Toppan, 1958)

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