'Various Concepts in a Metric Space' Video Lecture
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Course Video 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 Sp.. Completion of Metric Spaces + Tutorial Vector Spaces with Examples Normed Spaces with Examples Banach Spaces and Schauder Basic Finite Dimensional Normed Spaces and Subspace.. 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 Sequ.. Representation of Functionals on a Hilbert Sp.. 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.. Baires Category & Uniform Boundedness Theorem.. Open Mapping Theorem Closed Graph Theorem Adjoint Operator Strong and Weak Convergence Convergence of Sequence of Operators and Func.. LP - Space LP - Space (Contd.)
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