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Course11110616046 lectures

Operator Theory

Prof. G. Ramesh · IIT Hyderabad

Start with lecture 1 At NPTEL

Lectures

week-01

  1. Semi Inner product spaces Video
  2. Inner Product Spaces Video
  3. Parallelogram law Video
  4. Hilbert Spaces Video
  5. Orthogonality Video
  6. Projection Theorem Video

week-02

  1. Linear Operator Video
  2. Bounded Operators Video
  3. Norm of a linear operator Video
  4. Examples of bounded operators Video
  5. The Adjoint Operator Video

week-03

  1. The adjoint: Properties Video
  2. Closed range operators-1 Video
  3. Closed range operators-2 Video
  4. Self-adjoint Operators Video
  5. Normal operators Video

week-04

  1. Isometris and Unitaries Video
  2. Isometris and Unitaries Video
  3. Mutually Orthogonal Projections Video
  4. Invariant Subspaces Video
  5. Monotone Convergence Theorem Video

week-05

  1. Square root Video
  2. Polar decomposition Video
  3. Invertibility Video
  4. Spectrum Video
  5. Spectral Mapping Theorem Video

week-07

  1. Decomposition of spectrum Video
  2. Computing spectrum: Examples Video
  3. Approximate spectrum Video
  4. Approximate spectrum: Properties Video
  5. Numerical bounds Video

week-08

  1. Compact Operators Video
  2. Compact Operators; Properties Video
  3. Spectral Theorem: Compact Self-Adjoint Operators Video
  4. Spectral Theorem: Consequences Video
  5. Compact Normal Operators Video

week-09

  1. Compact Operators Singular value Decomposition Video
  2. Fredholm Alternative Theorem Video
  3. Orthogonal decomposition of self-adjoint operators Video
  4. Spectral family; Properties-I Video
  5. Lecture 5: Spectral family; Properties-II Video

week-10

  1. Spectral theorem Self adjoint Operators Video
  2. Spectral theorem Examples Video
  3. Spectral theorem: Consequences Video
  4. Continuous functional Calculus Video
  5. Spectral mapping theorem Video

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Hyderabad
Department
Mathematics
Teacher
Prof. G. Ramesh
Level
Undergraduate
Language
English
Subjects
Mathematics
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge. Coordinated by IIT Madras.
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