Course Contents
Linear space, norm, normed linear space, Banach space and examples, Quotient spaces, Finite dimensional Normed Spaces and Subspaces, Compactness and finite dimension, equivalance of norms. Continuous and bounded linear operators on spaces. Linear functionals, Dual of a normed space, linear operators and linear functionals on finite dimensional normed spaces. Inner product spaces, Hilbert spaces with examples. Orthogonal complements and direct sums, Orthonormal sets and sequences. Conjugate spaces, representation of linear functional on Hilbert space, Reflexive Spaces. Projections, Adjoint of an operator.
Course Learning Outcomes
This course will enable the student to apply ideas involved in functional analysis to familiar and to novel situations, work with abstract concepts and in a context of generality, reason logically and work analytically, perform with high levels of accuracy and transfer expertise between different topics in mathematics.
lecture 2
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Lecture 1
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Lecture 3
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Lecture 4
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Lecture 5
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Lecture 6
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Lecture 7
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Book Title : Introductory Functional Analysis with Applications
Author : E. Kreyszig
Edition :
Publisher : John Wiley, New York
Book Title : Functional Analysis
Author : Y. Eidelman, V. D. Milman and A. Tsolomitis
Edition :
Publisher :
Book Title : Introductory Functional Analysis with Applications
Author : E. Kreyszig
Edition : ---
Publisher : John Wiley, New York
View Now
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