Noncommutative Analysis

Tag: operator theory

Michael Hartz awarded Zemanek prize in functional analysis

Idly skimming through the September issue of the Newsletter of the European Mathematical Society, I stumbled upon the very happy announcement that the 2020 Jaroslav and Barbara Zemanek prize in functional analysis with emphasis on operator theory was awarded to Michael Hartz.

The breakthrough result that every complete Nevanlinna-Pick space has the column-row property is one of his latest results and has appeared on the arxiv this May. Besides solving an interesting open problem, it is a really elegant and strong paper.

It is satisfying to see a young and very talented mathematician get recognition!

Full disclosure 😉 Michael is a sort of mathematical relative (he was a PhD student of my postdoc supervisor Ken Davidson), a collaborator (together with Ken Davidson we wrote the paper Multipliers of embedded discs) and a friend. I have to boast that from the moment that I heard about him I knew that he will do great things – in his first paper, which he wrote as a masters student, he ingeniously solved an open problem of Davidson, Ramsey and myself. Since then he has worked a lot on some problems that are close to my interests, and I have been following him with admiration.

Congratulations Michael!

The complex matrix cube problem summer project – summary of results

In the previous post I announced the project that I was going to supervise in the Summer Projects in Mathematics week at the Technion. In this post I wish to share what we did and what we found in that week.

I had the privilege to work with two very bright students who have recently finished their undergraduate studies: Mattya Ben-Efraim (from Bar-Ilan University) and Yuval Yifrach (from the Technion). It is remarkable the amount of stuff they learned for this one week project (the basics of C*-algebras and operator spaces), and that they actually helped settle the question that I raised to them.

I learned a lot of things in this project. First, I learned that my conjecture was false! I also learned and re-learned some programming abilities, and I learned something about the subtleties and limitations of numerical experimentation (I also learned something about how to supervise an undergraduate research project, but that’s besides the point right now).

Statement of the problem

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The remarkable Hilbert space H^2 (part III – three open problems)

This is the last in the series of three posts on the d–shift space, which accompany/replace the colloquium talk I was supposed to give. The first two parts are available here and here. In this post I will discuss three open problems that I have been thinking about, which are formulated within the setting of H^2_d.

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The remarkable Hilbert space H^2 (Part II – multivariable operator theory and model theory)

This post is the second post in the series of posts on the d–shift space, a.k.a. the Drury–Arveson space, a.k.a. H^2_d (see this previous post about the space H^2).

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Functional Analysis – Introduction. Part I

I begin by making clear a certain point. Functional analysis is an enormous branch of mathematics, so big that it does not seem appropriate to call it “a branch”, it sometimes looks more like another tree. When I will talk below about functional analysis, I will mean “textbook functional analysis” and not “research functional analysis”. By this I mean that I will only refer to the core of the theory which is several decades old and which is more-or-less agreed to be the essential and basic part of the subject.

The goal of this post is to serve as an introduction to the course “Advanced Analysis, 201.2.5401”, which is a basic graduate course on (textbook) functional analysis. In the lectures I will only have time to give a limited description of the roots of the subject and the motivation will have to be brief. Here I will aim to describe what was the climate in which this tree grew, where are its roots and what are its fruits.

To prepare this introduction I am relying on the following sources. First and foremost, my love of the subject and my point of view on it were strongly shaped by my teachers, and in particular by Boris Paneah (my Master’s thesis advisor) and Baruch Solel (my PhD. thesis advisor). Second, I learned a lot on the subject from the book “Mathematical Thought from Ancient to Modern Times” by M. Kline and from the notes sections of Rudin’s and Reed-Simon’s books “Functional Analysis”.

And a warning to the kids: this is a blog, not a book, and if you really want to learn something go read the books (the books I mentioned have precise references).

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