Noncommutative Analysis

Tag: von Neumann algebra

Introduction to von Neumann algebras, Lecture 1 (Introduction to the course, and a crash course in operator algebras, the spectral theorem)

1. Micro prologue

Perhaps we cannot start a course on von Neumann algebras, without making a few historical notes about the beginning of the theory.

(To say it more honestly and openly, what I wanted to say is that perhaps I cannot teach a course on von Neumann algebras without finally reading the classical works by von Neumann and also learning a bit about the man. von Neumann was a true genius and has contributed all over mathematics, see the Wikipedia article).

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Souvenirs from Bangalore

I recently returned from the two week long workshop and conference Recent Advances in Operator Theory and Operator Algebras which took place in ISI Bangalore. As I promised myself before going, I was on the look-out for something new to be excited about and to learn. The event (beautifully organized and run) was made of two parts: a workshop, which was a one week mini-school on several topics (see here for topics) and a one week conference. It was very very broad, and there were several talks (or informal discussions) which I plan to pursue further.

In this post and also perhaps in a future one I will try to work out (for my own benefit, mostly) some details of a small part of the research presented in two of the talks. The first part is the Superproduct Systems which arise in the theory of E_0-semigroups on type II_1 factors (following the talk of R. Srinivasan). The second (which I will not discuss here, but perhpas in the future) is the equivalence between the Baby Corona Theorem and the Full Corona Theorem (following the mini-course given by B. Wick). In neither case will I describe the most important aspect of the work, but something that I felt was urgent for me to learn. 

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