Lecture 16 of 40Functional Analysis
Concept of Algebraic Dual and Reflexive Space
Prof. P.D. Srivastava · IIT Kharagpur
Credits and licence
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- Functional Analysis, IIT Kharagpur (at NPTEL)
- Licence
- CC BY-NC-SA, as NPTEL states it. Non-commercial use only.
- Attribution
- NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
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- Tweens profiles and older. How courses are placed
All the lectures
- Metric Spaces with Examples
- Holder Inequality and Minkowski Inequality
- Various Concepts in a Metric Space
- Separable Metrics Spaces with Examples
- Convergence, Cauchy Sequence, Completeness
- Examples of Complete and Incomplete Metric Spaces
- Completion of Metric Spaces + Tutorial
- Vector Spaces with Examples
- Normed Spaces with Examples
- Banach Spaces and Schauder Basic
- Finite Dimensional Normed Spaces and Subspaces
- Compactness of Metric/Normed Spaces
- Linear Operators-definition and Examples
- Bounded Linear Operators in a Normed Space
- Bounded Linear Functionals in a Normed Space
- Concept of Algebraic Dual and Reflexive Space
- Dual Basis & Algebraic Reflexive Space
- Dual Spaces with Examples
- Tutorial - I
- Tutorial - II
- Inner Product & Hilbert Space
- Further Properties of Inner Product Spaces
- Projection Theorem, Orthonormal Sets and Sequences
- Representation of Functionals on a Hilbert Spaces
- Hilbert Adjoint Operator
- Self Adjoint, Unitary & Normal Operators
- Tutorial - III
- Annihilator in an IPS
- Total Orthonormal Sets And Sequences
- Partially Ordered Set and Zorns Lemma
- Hahn Banach Theorem for Real Vector Spaces
- Hahn Banach Theorem for Complex V.S. & Normed Spaces
- Baires Category & Uniform Boundedness Theorems
- Open Mapping Theorem
- Closed Graph Theorem
- Adjoint Operator
- Strong and Weak Convergence
- Convergence of Sequence of Operators and Functionals
- LP - Space
- LP - Space (Contd.)