NOC:C* Algebras and Spectral Theorem

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