Learn · C* Algebras and Spectral Theorem
Lecture 9 of 40Week 2 Banach algebras and Gelfand transform
Gelfand transform-I
Prof. E K Narayanan · IISc Bangalore
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All the lectures
- Finite dimensional Spectral theorem
- Compact operators
- Spectral theorem for Compact self-adjoint operators
- Spectral theorem for compact Normal operators
- Banach algebras
- Gelfand-Mazur theorem
- Spectral radius
- Multiplicative functionals
- Gelfand transform-I
- Gelfand transform -II
- C* algebras
- Examples and Wiener’s theorem
- Gelfand-Naimark theorem
- Non-unital Banach algebras
- Non-unital C* algebra
- Gelfand transform of non-unital C*algebras
- Gelfand-Naimark theorem for non-unital C* algebras
- Continuous functional calculus
- Bounded functional calculus -I
- Bounded functional calculus -II
- Projection valued measures
- Bounded functional calculus with respect to a projection valued measure
- Spectral Theorem I
- Spectral theorem II
- Some applications
- Spectral theorem for a bounded normal operator
- Resolution of identity -I
- Resolution of identity -II
- Resolution of identity-III
- Resolution of identity-IV
- Equivalence of various forms of spectral theorems -I
- Equivalence of various forms of spectral theorems -II
- Spectrum of a self-adjoint operator-I
- Spectrum of a self-adjoint operator-II
- Commuting family of self-adjoint operators
- Continuous functional calculus for commuting family of self-adjoint operators -I
- Continuous functional calculus for commuting family of self-adjoint operators -II
- Fuglede’s theorem
- Spectral theorem for commuting finite family of normal operators
- Multiplicity theory