Functional Analysis 8G1C5N5RBV

URI	`m2://res/8G1C5N5RBV`
Kind	course
Creators	Kesavan (instructor)
Date	2021-06-08
Scope	in

Expressions

e1: edition

Language	en
Date	2021-06-08

m1: page, IMSc (record). nptel 111106147
m2: page, 2021-06-08 (record). nptel 111106147

Contents

part 1: Week 1
session 1: 1.1: Normed Linear Spaces
session 2: 1.2: Examples of Normed Linear Spaces
session 3: 1.3: Examples, contd...
session 4: 1.4: Continuous linear maps - Part 1
session 5: 1.5: Continuous linear maps - Part 2
session 6: 1.6: Isomorphisms
part 2: Week 2
session 7: 2.1 - Exercises
session 8: 2.2 - Exercises (contd.)
session 9: 2.3 - Hahn-Banach Theorems
session 10: 2.4 - Reflexivity
session 11: 2.5 - Geometric version
part 3: Week 3
session 12: 3.1 - Geometric version (contd.)
session 13: 3.2 - Vector valued integration
session 14: 3.3 - Exercises - Part 1
session 15: 3.4 - Exercises - Part 2
session 16: 3.5 - Baire's Theorem and Applications
part 4: Week 4
session 17: 4.1 - Application to Fourier series
session 18: 4.2 - Open mapping and closed graph theorems
session 19: 4.3 - Annihilators
session 20: 4.4 - Complemented subspaces
session 21: 4.5 - Unbounded Operators, Adjoints - Part 1
session 22: 4.6 - Unbounded Operators, Adjoints - Part 2
part 5: Week 5
session 23: 5.1 - Orthogonality relations
session 24: 5.2 - Exercises
session 25: 5.3 - Exercises (contd.)
session 26: 5.4 - Weak topology - Part 1
session 27: 5.5 - Weak topology - Part 2
session 28: 5.7 - Weak topology - Part 3
part 6: Week 6
session 29: 6.1 - Weak* topology - Part 1
session 30: 6.2 - Weak* topology - Part 2
session 31: 6.3 - Reflexive Spaces
session 32: 6.4 - Separable Spaces - Part 1
session 33: 6.5 - Separable Spaces - Part 2
session 34: 6.6 - Uniformly Convex Spaces
session 35: 6.7 - Applications
part 7: Week 7
session 36: 7.1 - Exercises
session 37: 7.2 - L-p Spaces - Part 1
session 38: 7.3 - L-p Spaces - Part 2
session 39: 7.4 - Completeness
session 40: 7.5 -Duality
session 41: 7.6 - L-p Spaces in Euclidean spaces - Part 1
session 42: 7.7 - L-p Spaces in Euclidean spaces - Part 2
part 8: Week 8
session 43: 8.1 - Dual of L-1
session 44: 8.2 - The space L-1 (contd.)
session 45: 8.3 - Exercises - Part 1
session 46: 8.4 - Exercises - Part 2
session 47: 8.5 - Exercises - Part 3
session 48: 8.6 - Exercises - Part 4
part 9: Week 9
session 49: 9.1 - Hilbert spaces - Part 1
session 50: 9.2 - Hilbert spaces - Part 2
session 51: 9.3 - Duality
session 52: 9.4 - Adjoints
session 53: 9.5 - Applications
session 54: 9.6 - Orthonormal sets
part 10: Week 10
session 55: 10.1 - Orthonormal bases - Part 1
session 56: 10.2 - Orthonormal bases - Part 2
session 57: 10.3 -Fourier series
session 58: 10.4 - Spectrum of an operator - Part 1
session 59: 10.5 - Spectrum of an operator - Part 2
session 60: 10.6 - Exercises - Part 1
part 11: Week 11
session 61: 11.1 - Exercises - Part 2
session 62: 11.2 - Exercises - Part 3
session 63: 11.3 - Compact operators - Part 1
session 64: 11.4 - Compact operators - Part 2
session 65: 11.5 - Riesz-Fredholm theory - Part 1
session 66: 11.6 -Riesz-Fredholm theory - Part 2
part 12: Week 12
session 67: 12.1 - Riesz-Fredholm theory
session 68: 12.2 - Spectrum of a compact operator
session 69: 12.3 - Spectrum of a compact self-adjoint operator
session 70: 12.4 - Eigenvalues of a compact self-adjoint operator
session 71: 12.5 - Exercises - Part 1
session 72: 12.6 - Exercises - Part 2
session 73: 12.7 - Exercises - Part 3
session 74: 12.8 - Exercises - Part 4

Catalogue records

nptel: 111106147 (manifestation)
nptel_video: 111106147 (manifestation)