Media Storage Type : 32 GB USB Stick
NPTEL Subject Matter Expert : Prof. E K Narayanan
NPTEL Co-ordinating Institute : IISc Bangalore
NPTEL Lecture Count : 40
NPTEL Course Size : 6.0 GB
NPTEL PDF Text Transcription : Available and Included
NPTEL Subtitle Transcription : Available and Included (SRT)
Lecture Titles:
Lecture 1 - Finite dimensional Spectral theorem
Lecture 2 - Compact operators
Lecture 3 - Spectral theorem for Compact self-adjoint operators
Lecture 4 - Spectral theorem for Compact Normal operators
Lecture 5 - Banach algebras
Lecture 6 - Gelfand-Mazur theorem
Lecture 7 - Spectral radius
Lecture 8 - Multiplicative functionals
Lecture 9 - Gelfand transform - I
Lecture 10 - Gelfand transform - II
Lecture 11 - C* algebras
Lecture 12 - Examples and Wiener’s theorem
Lecture 13 - Gelfand-Naimark theorem
Lecture 14 - Non-unital Banach algebras
Lecture 15 - Non-unital C* algebra
Lecture 16 - Gelfand transform of non-unital C*algebras
Lecture 17 - Gelfand-Naimark theorem for non-unital C* algebras
Lecture 18 - Continuous functional calculus
Lecture 19 - Bounded functional calculus - I
Lecture 20 - Bounded functional calculus - II
Lecture 21 - Projection valued measures
Lecture 22 - Bounded functional calculus with respect to a projection valued measure
Lecture 23 - Spectral Theorem - I
Lecture 24 - Spectral theorem - II
Lecture 25 - Some applications
Lecture 26 - Spectral theorem for a bounded normal operator
Lecture 27 - Resolution of identity - I
Lecture 28 - Resolution of identity - II
Lecture 29 - Resolution of identity - III
Lecture 30 - Resolution of identity - IV
Lecture 31 - Equivalence of various forms of spectral theorems - I
Lecture 32 - Equivalence of various forms of spectral theorems - II
Lecture 33 - Spectrum of a self-adjoint operator - I
Lecture 34 - Spectrum of a self-adjoint operator - II
Lecture 35 - Commuting family of self-adjoint operators
Lecture 36 - Continuous functional calculus for commuting family of self-adjoint operators - I
Lecture 37 - Continuous functional calculus for commuting family of self-adjoint operators - II
Lecture 38 - Fuglede’s theorem
Lecture 39 - Spectral theorem for commuting finite family of normal operators
Lecture 40 - Multiplicity theory