Noncommutative Analysis

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William Arveson

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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Hot morning for the Technion in arxiv math.OA

While I am spending my morning preparing for a two week vacation in the very hot Park Hayarden, it is was nice to browse the arxiv mailing list for math.OA (Operator Algebras) and find four entries by operator-people from the Technion. I don’t recall such a nice coincidence happening before.

There are two very interesting new submissions:

  1. Hyperrigid subsets of graph C*-algebras and the property of rigidity at 0“, by our PhD. student Guy Salomon.
  2. On fixed points of self maps of the free ball” by recently-become-ex postdoc Eli Shamovich.

There is also a cross listing (from Spectral Theory) to the paper “Spectral Continuity for Aperiodic Quantum Systems I. General Theory“, by Siegfried Beckus (a postdoc in our department) together with Jean Bellissard and Giuseppe De Nittis.

Finally, there is a new (and final) version of the paper “Compact Group Actions on Topological and Noncommutative Joins” by Benjamin Passer (another postdoc in our department) together with Alexandru Chirvasitu.

 

Aleman, Hartz, McCarthy and Richter characterize interpolating sequences in complete Pick spaces

The purpose of this post is to discuss the recent important contribution by Aleman, Hartz, McCarthy and Richter to the characterization of interpolating sequences (for multiplier algebras of certain Hilbert function spaces). Their recent paper “Interpolating sequences in spaces with the complete Pick property” was uploaded to the arxiv about two weeks ago; here I will just give some background and state the main result. (Even more recently these four authors released yet another paper that looks very interesting – this one.)

1. Background – interpolating sequences

We will be working with the notion of Hilbert function spaces – also called reproducing Hilbert spaces (see this post for an introduction). Suppose that H is a Hilbert function space on a set X, and k its reproducing kernel. The Pick interpolation problem is the following:

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Multivariable Operator Theory workshop at the Technion (Haifa, June 2017)

I am happy to advertise the research workshop Multivariable Operator Theory, that will take place at the Technion, In June 18-22, 2017, on the occasion of Baruch Solel’s 65 birthday. Here is the workshop webpage, and here is a link to the poster. The website and poster contain a preliminary list of speakers, and some words of explanation of what the workshop is about, roughly.

The workshop proper (that is: lectures) will take place from Monday June 19 to Thursday June 22, morning to evening. Everyone is welcome to attend, and there is no registration fee, but if you are planning to come you better contact me so we make sure that there is enough room in the lecture room, enough fruit and cookies in the breaks, etc. The information on the website will be updated from time to time, and will probably converge as the time of the workshop comes near.

Please free to contact me if you have any questions.

Summer projects in math at the Technion 2016

This year, the Faculty of Math at the Technion is continuing with its recently founded tradition of summer projects. As in last year’s week of summer projects, the Faculty of Math at the Technion is inviting advanced undergraduates from Israel and from around the world to get a little taste of research in mathematics. This is a nice opportunity, especially for someone who is considering graduate studies in math.

For a list of topics with abstracts, and for other important details (like how to apply), see this page.