HNGU M.SC. MATHEMATICS SEMESTER - 3
MSM1301 β FUNCTIONAL ANALYSIS - 1
Unit 1:
- Normed linear space: definition and examples,
- continuous linear transformations,
- Spaces BL(X,Y), BL(X) and BL(X,X),
- lp & Lp (for 0Β£pΒ£Γ) Banach spaces.
Unit 2:
- Hahn-Banach theorem and its applications,
- Open mapping theorem,
- Dual normed spaces,
- Natural imbedding of normed space into double dual space of normed spaces.
Unit 3:
- Closed graph theorem,
- Uniform boundedness principle,
- Conjugate of an operator,
- Bounded inverse mapping theorem.
Unit 4:
- Hilbert space: definition and examples,
- Orthogonal complement,
- Orthonormal set,
- Besselβs inequality,
- Projection theorem,
- Riesz Representation theorem.
Download Reference Books:
Note: The course is roughly
covered by the following books:
Introduction to Topology and Modern Analysis - G. F. Simmons, Tata McGraw,1963
1. Functional Analysis 2nd Edition - B. V. Limaye, New Age International Ltd. Publishers.
2. First course in Functional Analysis - Goffman and George Padre, Prentice Hall of India.
3. Principles of Functional Analysis - Martin Schechter (student edition) Academic Press, N Y.
4. Lectures in Functional Analysis and Operator theory - S. K. Berberain, Springer Verlag.
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