Course Details
Subject {L-T-P / C} : MA5101 : Functional Analysis { 3-0-0 / 3}
Subject Nature : Theory
Coordinator : Prof. Shesadev Pradhan
Syllabus
Normed spaces, Banach spaces, properties of normed spaces, Compactness and finite dimension, Bounded and continuous linear operators, Hahn-Banach theorem and its applications, Open mapping and closed graph Theorem, Representation of Dual spaces , Bounded and Copmpact Operator, Adjoint operators, Spectrum and Gelfund- Mazur Theorem. Weak Topology and Banach-Alaoglu Theorem, Reflexiv spaces.
Inner product spaces, Hilbert spaces, Representation of functionals on Hilbert spaces, Adjoint operator, Self-adjoint, unitary operators, Spectrum.
Course Objectives
- NA
- na
Course Outcomes
na
Essential Reading
- B. V. Limaye, Functional Analysis, New Age International, 1996.
- NA, NA, NA
Supplementary Reading
- Y. Eidelman, V. D. Milman, A. Tsolomitis, Functional Analysis: An Introduction, AMS Bookstore, 2004.
- E. Kreyszig, , Introductory Functional Analysis with Applications, Wiley, 1978