Math 2.0

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C* algebras and spectral theorem V1TS5TW679

URIm2://res/V1TS5TW679
Kindcourse
CreatorsE K Narayanan (instructor)
Date2023-02-07
Scopein
Idscourse 04dese585:111108164

Expressions

e1: edition

Languageen
Date2023-02-07
Contents
  • part 1: Week 1 Spectral theorem For compact operators
  • session 1: Finite dimensional Spectral theorem
  • session 2: Compact operators
  • session 3: Spectral theorem for Compact self-adjoint operators
  • session 4: Spectral theorem for compact Normal operators
  • part 2: Week 2 Banach algebras and Gelfand transform
  • session 5: Banach algebras
  • session 6: Gelfand-Mazur theorem
  • session 7: Spectral radius
  • session 8: Multiplicative functionals
  • session 9: Gelfand transform-I
  • session 10: Gelfand transform -II
  • part 3: Week 3 Gelfand-Naimark theorem
  • session 11: C* algebras
  • session 12: Examples and Wiener’s theorem
  • session 13: Gelfand-Naimark theorem
  • session 14: Non-unital Banach algebras
  • session 15: Non-unital C* algebra
  • part 4: Week 4 Gelfand-Naimark theorem And functional calculus
  • session 16: Gelfand transform of non-unital C*algebras
  • session 17: Gelfand-Naimark theorem for non-unital C* algebras
  • session 18: Continuous functional calculus
  • session 19: Bounded functional calculus -I
  • session 20: Bounded functional calculus -II
  • part 5: Week 5 Spectral theorem for commutative C* sub algebras Of operators
  • session 21: Projection valued measures
  • session 22: Bounded functional calculus with respect to a projection valued measure
  • session 23: Spectral Theorem I
  • session 24: Spectral theorem II
  • session 25: Some applications
  • part 6: Week 6 Spectral theorem and Resolution of identity
  • session 26: Spectral theorem for a bounded normal operator
  • session 27: Resolution of identity -I
  • session 28: Resolution of identity -II
  • session 29: Resolution of identity-III
  • session 30: Resolution of identity-IV
  • part 7: Week 7 Equivalence of various forms of spectral theorems And commuting families
  • session 31: Equivalence of various forms of spectral theorems -I
  • session 32: Equivalence of various forms of spectral theorems -II
  • session 33: Spectrum of a self-adjoint operator-I
  • session 34: Spectrum of a self-adjoint operator-II
  • session 35: Commuting family of self-adjoint operators
  • part 8: Week 8 Spectral theorem for a commuting family of Normal operators
  • session 36: Continuous functional calculus for commuting family of self-adjoint operators -I
  • session 37: Continuous functional calculus for commuting family of self-adjoint operators -II
  • session 38: Fuglede’s theorem
  • session 39: Spectral theorem for commuting finite family of normal operators
  • session 40: Multiplicity theory

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