A survey on the Drury-Arveson space, and a new paper

by Orr Shalit

I just finished writing (and re-writing) a survey paper on the Drury-Arveson space. Here it is. I am posting a link to this survey in hope that it will be useful for somebody (I also need to figure in what open online form I am going to keep this article). I will also be very happy to hear comments about mistakes or glaring omissions I made. I am planning to submit this survey to a handbook in operator theory project, and there are some places in the text such as :”SEE CHAPTER ON DILATION THEORY” which is supposed to refer to other chapters in the handbook.

This is the first time that I am writing such a comprehensive survey article, and it is much, much harder than I thought it would be. The hardest part is to find the balance of which references to give and which references not to give. A survey as it is cannot contain all information, and I think that a good survey should make it clear to the reader which are the most important references. That’s a big responsibility!

I wrote a series of blog posts on Drury-Arveson space: one, two and three. Actually, at the time I wrote those posts I already knew that I was going to write this survey, and it was kind of a warm up.

I take this opportunity also to put up a link to this a new paper By Michael Hartz, Ken Davidson and myself, “Multipliers of embedded discs”. In this paper we continue our journey to understand the algebraic structure of complete Pick algebras in terms of the varieties on which they naturally live, I explained this problem in this older post.