William Arveson

by Orr Shalit

I came back to this old post, and noticed that it is almost ten years since Bill Arveson passed away. It’s hard to believe.

Noncommutative Analysis

William B. Arveson was born in 1934 and died last year on November 15, 2011. He was my mathematical hero; his written mathematics has influenced me more than anybody else’s. Of course, he has been much more than just my hero, his work has had deep and wide influence on the entire operator theory and operator algebras communities. Let me quickly give an example that everyone can appreciate: Arveson proved what may be considered as the “Hahn-Banach Theorem” appropriate for operator algebras. He did much more than that, and I will expand below on some of his early contributions, but I want to say something before that on what he was to me.

When I was a PhD student I worked in noncommutative dynamics. Briefly, this is the study of actions of (one-parameter) semigroups of *-endomorphisms on von Neumann algebras (in short E-semigroups). The definitive book on this subject is…

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