NOC:Operator Theory

Lecture 1 - Semi Inner product spaces

Lecture 2 - Inner Product Spaces

Lecture 3 - Parallelogram law

Lecture 4 - Hilbert Spaces

Lecture 5 - Orthogonality

Lecture 6 - Projection Theorem

Lecture 7 - Linear Operator

Lecture 8 - Bounded Operators

Lecture 9 - Norm of a linear operator

Lecture 10 - Examples of bounded operators

Lecture 11 - The Adjoint Operator

Lecture 12 - The Adjoint: Properties

Lecture 13 - Closed range operators - 1

Lecture 14 - Closed range operators - 2

Lecture 15 - Self-adjoint Operators

Lecture 16 - Normal operators

Lecture 17 - Isometris and Unitaries

Lecture 18 - Isometris and Unitaries

Lecture 19 - Mutually Orthogonal Projections

Lecture 20 - Invariant Subspaces

Lecture 21 - Monotone Convergence Theorem

Lecture 22 - Square root

Lecture 23 - Polar decomposition

Lecture 24 - Invertibility

Lecture 25 - Spectrum

Lecture 26 - Spectral Mapping Theorem

Lecture 27 - The spectral radius formula

Lecture 28 - multiplicative linear functionals

Lecture 29 - The GKZ-theorem

Lecture 30 - Maximal Ideal Space

Lecture 31 - Commutative C*-algebras

Lecture 32 - Decomposition of spectrum

Lecture 33 - Computing spectrum: Examples

Lecture 34 - Approximate spectrum

Lecture 35 - Approximate spectrum: Properties

Lecture 36 - Numerical bounds

Lecture 37 - Compact Operators

Lecture 38 - Compact Operators; Properties

Lecture 39 - Spectral Theorem: Compact Self-Adjoint Operators

Lecture 40 - Spectral Theorem: Consequences

Lecture 41 - Compact Normal Operators

Lecture 42 - Compact Operators Singular value Decomposition

Lecture 43 - Fredholm Alternative Theorem

Lecture 44 - Orthogonal decomposition of self-adjoint operators

Lecture 45 - Spectral family; Properties - I

Lecture 46 - Spectral family; Properties - II

Lecture 47 - Spectral theorem Self adjoint Operators

Lecture 48 - Spectral theorem Examples

Lecture 49 - Spectral theorem: Consequences

Lecture 50 - Continuous functional Calculus

Lecture 51 - Spectral mapping theorem