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More on Expectation

Expectation of Random Variables

Random Vectors, Distribution, Independence etc.

Probability Mass functions (Examples)

Discrete Random Variables

Conditional probability

We discuss the basic framework of the theory of probability.

Type II-Infinity Factors

Tomita-Takesaki theory for II_1 factors

Towards the end the video got frozen due to unknown reasons.

Type I factors

Tensor product of Hilbert spaces, compressions of von Neumann algebras, etc

Polar decomposition

Infinite dimensional finite von Neumann algebras

Group von Neumann algebras

GNS Construction

von Neumann algebras

Spectral theorem for normal operators

Joint Spectrum of commuting self adjoint operators

Spectral projections

Spectral theorem for self-adjoint operators.

Strong continuity of representation of L^\\infty

Representations of C(X)

C*-algebras

Banach algebras, spectrum, spectral radius formula.

Preliminaries on Hilbert spaces -1

Uniform Convergence, Fejer's Theorem etc

Uniform boundedness principle, divergent Fourier series

Hilbert spaces, Orthonormal basis etc