Lecture 44 of 74Week 8
8.2 - The space L-1 (contd.)
Prof. Kesavan · IMSc
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- Functional Analysis, IMSc (at NPTEL)
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- CC BY-NC-SA, as NPTEL states it. Non-commercial use only.
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- NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge. Coordinated by IIT Madras.
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All the lectures
- 1.1: Normed Linear Spaces
- 1.2: Examples of Normed Linear Spaces
- 1.3: Examples, contd...
- 1.4: Continuous linear maps - Part 1
- 1.5: Continuous linear maps - Part 2
- 1.6: Isomorphisms
- 2.1 - Exercises
- 2.2 - Exercises (contd.)
- 2.3 - Hahn-Banach Theorems
- 2.4 - Reflexivity
- 2.5 - Geometric version
- 3.1 - Geometric version (contd.)
- 3.2 - Vector valued integration
- 3.3 - Exercises - Part 1
- 3.4 - Exercises - Part 2
- 3.5 - Baire's Theorem and Applications
- 4.1 - Application to Fourier series
- 4.2 - Open mapping and closed graph theorems
- 4.3 - Annihilators
- 4.4 - Complemented subspaces
- 4.5 - Unbounded Operators, Adjoints - Part 1
- 4.6 - Unbounded Operators, Adjoints - Part 2
- 5.1 - Orthogonality relations
- 5.2 - Exercises
- 5.3 - Exercises (contd.)
- 5.4 - Weak topology - Part 1
- 5.5 - Weak topology - Part 2
- 5.7 - Weak topology - Part 3
- 6.1 - Weak* topology - Part 1
- 6.2 - Weak* topology - Part 2
- 6.3 - Reflexive Spaces
- 6.4 - Separable Spaces - Part 1
- 6.5 - Separable Spaces - Part 2
- 6.6 - Uniformly Convex Spaces
- 6.7 - Applications
- 7.1 - Exercises
- 7.2 - L-p Spaces - Part 1
- 7.3 - L-p Spaces - Part 2
- 7.4 - Completeness
- 7.5 -Duality
- 7.6 - L-p Spaces in Euclidean spaces - Part 1
- 7.7 - L-p Spaces in Euclidean spaces - Part 2
- 8.1 - Dual of L-1
- 8.2 - The space L-1 (contd.)
- 8.3 - Exercises - Part 1
- 8.4 - Exercises - Part 2
- 8.5 - Exercises - Part 3
- 8.6 - Exercises - Part 4
- 9.1 - Hilbert spaces - Part 1
- 9.2 - Hilbert spaces - Part 2
- 9.3 - Duality
- 9.4 - Adjoints
- 9.5 - Applications
- 9.6 - Orthonormal sets
- 10.1 - Orthonormal bases - Part 1
- 10.2 - Orthonormal bases - Part 2
- 10.3 -Fourier series
- 10.4 - Spectrum of an operator - Part 1
- 10.5 - Spectrum of an operator - Part 2
- 10.6 - Exercises - Part 1
- 11.1 - Exercises - Part 2
- 11.2 - Exercises - Part 3
- 11.3 - Compact operators - Part 1
- 11.4 - Compact operators - Part 2
- 11.5 - Riesz-Fredholm theory - Part 1
- 11.6 -Riesz-Fredholm theory - Part 2
- 12.1 - Riesz-Fredholm theory
- 12.2 - Spectrum of a compact operator
- 12.3 - Spectrum of a compact self-adjoint operator
- 12.4 - Eigenvalues of a compact self-adjoint operator
- 12.5 - Exercises - Part 1
- 12.6 - Exercises - Part 2
- 12.7 - Exercises - Part 3
- 12.8 - Exercises - Part 4