Operator Theory XNEPKJANC4

URI	`m2://res/XNEPKJANC4`
Kind	course
Creators	G. Ramesh (instructor)
Date	2022-09-26
Scope	in

Expressions

e1: edition

Language	en
Date	2022-09-26

m1: page, IIT Hyderabad (record). nptel 111106160
m2: page, 2022-09-26 (record). nptel 111106160

Contents

part 1: week-01
session 1: Semi Inner product spaces
session 2: Inner Product Spaces
session 3: Parallelogram law
session 4: Hilbert Spaces
session 5: Orthogonality
session 6: Projection Theorem
part 2: week-02
session 7: Linear Operator
session 8: Bounded Operators
session 9: Norm of a linear operator
session 10: Examples of bounded operators
session 11: The Adjoint Operator
part 3: week-03
session 12: The adjoint: Properties
session 13: Closed range operators-1
session 14: Closed range operators-2
session 15: Self-adjoint Operators
session 16: Normal operators
part 4: week-04
session 17: Isometris and Unitaries
session 18: Isometris and Unitaries
session 19: Mutually Orthogonal Projections
session 20: Invariant Subspaces
session 21: Monotone Convergence Theorem
part 5: week-05
session 22: Square root
session 23: Polar decomposition
session 24: Invertibility
session 25: Spectrum
session 26: Spectral Mapping Theorem
part 6: week-07
session 27: Decomposition of spectrum
session 28: Computing spectrum: Examples
session 29: Approximate spectrum
session 30: Approximate spectrum: Properties
session 31: Numerical bounds
part 7: week-08
session 32: Compact Operators
session 33: Compact Operators; Properties
session 34: Spectral Theorem: Compact Self-Adjoint Operators
session 35: Spectral Theorem: Consequences
session 36: Compact Normal Operators
part 8: week-09
session 37: Compact Operators Singular value Decomposition
session 38: Fredholm Alternative Theorem
session 39: Orthogonal decomposition of self-adjoint operators
session 40: Spectral family; Properties-I
session 41: Lecture 5: Spectral family; Properties-II
part 9: week-10
session 42: Spectral theorem Self adjoint Operators
session 43: Spectral theorem Examples
session 44: Spectral theorem: Consequences
session 45: Continuous functional Calculus
session 46: Spectral mapping theorem

Catalogue records

nptel: 111106160 (manifestation)
nptel_video: 111106160 (manifestation)