COMPLETE SPACES (COMPLETE METRIC SPACE & COMPLETE SUBSPACE OF A METRIC SPACE, THEOREM)

COMPLETE SPACES (COMPLETE METRIC SPACE & COMPLETE SUBSPACE OF A METRIC SPACE, THEOREM)



Functional Analysis – I, 3 Cr. Hours,For students of B.S./M.Sc.Mathematics, and Engineering etc. PPSC, SPSC, KPPSC, BPSC, AJKPSC, FPSC/CSS.
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-Linear operators
7-Linear functionals
8- Finite dimensional normed spaces
9-Continuous or bounded linear operators
10-Dual spaces
CHAPTER-3: INNER PRODUCT SPACES
1-Definition and examples
2-Orthonormal sets and bases
3-Annihilators
4-Projections
5-Hilbert space
6-Linear functionals on Hilbert spaces
7-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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