# Functional Analysis Video Lectures

Functional Analysis
'Functional Analysis' Video Lectures by Prof. P.D. Srivastava from IIT Kharagpur
 "Functional Analysis" - Video Lectures 1. Metric Spaces with Examples 2. Holder Inequality and Minkowski Inequality 3. Various Concepts in a Metric Space 4. Separable Metrics Spaces with Examples 5. Convergence, Cauchy Sequence, Completeness 6. Examples of Complete and Incomplete Metric Spaces 7. Completion of Metric Spaces + Tutorial 8. Vector Spaces with Examples 9. Normed Spaces with Examples 10. Banach Spaces and Schauder Basic 11. Finite Dimensional Normed Spaces and Subspaces 12. Compactness of Metric/Normed Spaces 13. Linear Operators-definition and Examples 14. Bounded Linear Operators in a Normed Space 15. Bounded Linear Functionals in a Normed Space 16. Concept of Algebraic Dual and Reflexive Space 17. Dual Basis & Algebraic Reflexive Space 18. Dual Spaces with Examples 19. Tutorial - I 20. Tutorial - II 21. Inner Product & Hilbert Space 22. Further Properties of Inner Product Spaces 23. Projection Theorem, Orthonormal Sets and Sequences 24. Representation of Functionals on a Hilbert Spaces 25. Hilbert Adjoint Operator 26. Self Adjoint, Unitary & Normal Operators 27. Tutorial - III 28. Annihilator in an IPS 29. Total Orthonormal Sets And Sequences 30. Partially Ordered Set and Zorns Lemma 31. Hahn Banach Theorem for Real Vector Spaces 32. Hahn Banach Theorem for Complex V.S. & Normed Spaces 33. Baires Category & Uniform Boundedness Theorems 34. Open Mapping Theorem 35. Closed Graph Theorem 36. Adjoint Operator 37. Strong and Weak Convergence 38. Convergence of Sequence of Operators and Functionals 39. LP - Space 40. LP - Space (Contd.)
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