Operator Theory and Function Theory in Drury–Arveson Space and Its Quotients
By Michael Hartz, Orr Shalit. 2013
61 citations recorded by the source corpus.
The Drury-Arveson space $H^2_d$, also known as symmetric Fock space or the $d$-shift space, is a Hilbert function space that has a natural $d$-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.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/31d2e5d0edf61e2be81e2daa79a30b777f7b9168
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In Applied Mathematics
In Geometry and Topology
Citations in the corpus
- Multiplier algebras of complete Nevanlinna–Pick spaces: Dilations, boundary representations and hyperrigidity (2016, background): “The multivariate counterpart to this discussion takes place in the so-called DruryArveson space H(2) d on the open unit ball Bd ⊂ C [28, 39, 12], see also the survey [46].”
- Algebras of bounded noncommutative analytic functions on subvarieties of the noncommutative unit ball (2017, background): “Let d ∈ N ∪ {∞}, and let H(2) d denote the Drury–Arveson space, and let Md denote the multiplier algebra of the Drury–Arveson space (see the survey [77]).”
- Geometric Arveson-Douglas conjecture (2013, methodology): “See the recent survey paper by Shalit [23] for some more details and further information, as well as the original paper by Douglas [8] for more on the motivation and applications to K-homology and index theory.”