Operator theory and function theory in Drury-Arveson space and its quotients
Abstract
The Drury-Arveson space , also known as symmetric Fock space or the -shift space, is a Hilbert function space that has a natural -tuple of operators acting on it, which gives it the structure of a Hilbert module. This survey aims to introduce the Drury-Arveson space, to give a panoramic view of the main operator theoretic and function theoretic aspects of this space, and to describe the universal role that it plays in multivariable operator theory and in Pick interpolation theory.
Keywords
Cite
@article{arxiv.1308.1081,
title = {Operator theory and function theory in Drury-Arveson space and its quotients},
author = {Michael Hartz and Orr Shalit},
journal= {arXiv preprint arXiv:1308.1081},
year = {2025}
}
Comments
This is a significantly renewed version of the survey by Shalit that first appeared in 2014, with Hartz as a new co-author. The survey consists of a mildly updated version of the original survey together with an extensive survey incorporating new developments from the years 2014-2025 (to appear in the 2nd Edition of Operator Theory); 61 pages