Functional Analysis and its Applications 2Z5XCWWBPH

URI	`m2://res/2Z5XCWWBPH`
Kind	course
Creators	Akhilesh Prasad (instructor)
Date	2025-01-18
Scope	in

Expressions

e1: edition

Language	en
Date	2025-01-18

m1: page, IIT-ISM Dhanbad (record). nptel 111105610
m2: page, 2025-01-18 (record). nptel 111105610

Contents

part 1: Week : 01
session 1: Lecture 1: An Overview and Metric Spaces with Examples
session 2: Lecture 2: Basic Inequalities and their Applications
session 3: Lecture 3: Complete Metric Spaces with Examples
session 4: Lecture 4: Vector Spaces and Subspaces with Examples
session 5: Lecture 5: Linear Transformation with Examples
part 2: Week : 02
session 6: Lecture 6: Normed Linear Space and Pseudo-Normed Linear Space with Examples
session 7: Lecture 7: Convergence, Cauchy Sequence in Normed Linear Spaces and Banach Spaces with Examples
session 8: Lecture 8: Further examples of Banach Spaces
session 9: Lecture 9: The Linear Space C[a, b] as Normed Linear Space but not Banachspace
session 10: Lecture 10: The Linear Spaces ?p and ?? as Banach Spaces
part 3: Week : 03
session 11: Lecture 11: The Quotient Space as Banach Space
session 12: Lecture 12: The Lp spaces as Banach Spaces
session 13: Lecture 13: Bounded Linear Transformations and Equivalent Norms with Examples
session 14: Lecture 14: Norm of Bounded (Continuous) LinearTransformations and Some Related Theorems
session 15: Lecture 15: Continuity of Functions in Normed Linear Spaces and some related Theorems
part 4: Week : 04
session 16: Lecture 16: The set of all Bounded Linear Transformations of Normed Linear Space N into N? as a...
session 17: Lecture 17: Further Theorems on Bounded Linear Transformations
session 18: Lecture 18: Linear Functionals, Dual Vector Space and Dual Basis
session 19: Lecture 19: Continuous (Bounded) Linear Functionals on Normed linear spaces
session 20: Lecture 20: Consequences of Equivalent Norms with Examples and on a Finite-Dimensional space,....
part 5: Week : 05
session 21: Lecture 21: Further Theorems on Finite-Dimensional Normed Linear Spaces
session 22: Lecture 22: Dual Space of ?p^n, ?1^n and ??^n
session 23: Lecture 23: Dual Space of ?p is ?q
session 24: Lecture 24: Dual Space of ?1 is ??
session 25: Lecture 25: Dual Space of ????0 is ?1
part 6: Week : 06
session 26: Lecture 26: Dual Space of c is ?1
session 27: Lecture 27: Inner Product Space with Examples
session 28: Lecture 28: Further Example of Inner Product Space and Schwartz’s Inequality
session 29: Lecture 29: Continuity of Inner Product, Parallelogram Law and Polarization Identity
session 30: Lecture 30: Hilbert Space with Examples
part 7: Week : 07
session 31: Lecture 31: Application of Polarization Identity
session 32: Lecture 32: Applications of the Parallelogram Law
session 33: Lecture 33: Weak Convergence and Strong Convergence
session 34: Lecture 34: Orthogonality of Vectors
session 35: Lecture 35: Orthogonal Complement of an Orthogonal Complement
part 8: Week : 08
session 36: Lecture 36: The Orthogonal Decomposition (Projection) Theorem
session 37: Lecture 37: Orthonormal Sets in Hilbert Spaces and Bessel’s Inequality
session 38: Lecture 38: Complete Orthonormal Sets
session 39: Lecture 39: Further Theorems on Complete Orthonormal Sets and Riesz-Fischer Theorem
session 40: Lecture 40: Gram-Schmidt Orthogonalization Process
part 9: Week : 09
session 41: Lecture 41: The Conjugate Space H* and The Riesz Representation Theorem
session 42: Lecture 42: Further Theorems on Conjugate Space H*
session 43: Lecture 43: The Conjugate of an Operator
session 44: Lecture 44: The Adjoint of an Operator on a Hilbert Space
session 45: Lecture 45: Properties of Adjoint Operators on Hilbert Spaces
part 10: Week : 10
session 46: Lecture 46: Self Adjoint Operators
session 47: Lecture 47: Partially Ordered Set and Positive Operators
session 48: Lecture 48: Normal Operators
session 49: Lecture 49: Further Theorems of Normal Operators
session 50: Lecture 50: Unitary Operators
part 11: Week : 11
session 51: Lecture 51: Partial Order Relations, Total Order, Maximaland Minimal Elements, Zorn’s Lemma
session 52: Lecture 52: Hahn-Banach Theorem (Part-I)
session 53: Lecture 53: Hahn-Banach Theorem (Part-II) and Proofof the Main Theorem
session 54: Lecture 54: Sublinear Functional and GeneralizedHahn-Banach Theorem
session 55: Lecture 55: Uniform Boundedness Principle
part 12: Week : 12
session 56: Lecture 56: Application of the Uniform BoundednessPrinciple and Uniform Boundedness Principle.....
session 57: Lecture 57: Applications of Uniform Boundedness Principle for Continuous Linear Functionals
session 58: Lecture 58: Open Mapping Theorem
session 59: Lecture 59: Applications of Open Mapping Theorem
session 60: Lecture 60: The Closed Graph Theorem
part 13: Live Session
session 61: Live Session 25-02-2025
session 62: Live Session 18-03-2025
session 63: Live Session 11-04-2025

Catalogue records

nptel: 111105610 (manifestation)
nptel_video: 111105610 (manifestation)