A closer look at a Poisson-like condition on the Drury-Arveson space

2020 ◽  
Vol 148 (6) ◽  
pp. 2497-2507
Author(s):  
Quanlei Fang ◽  
Jingbo Xia
Keyword(s):  
Arveson Space

scholarly journals On a class of shift-invariant subspaces of the Drury-Arveson space

2018 ◽  
Vol 5 (1) ◽  
pp. 1-8
Author(s):  
Nicola Arcozzi ◽  
Matteo Levi
Keyword(s):  
Invariant Subspace ◽  
Invariant Subspaces ◽  
Hankel Operators ◽  
Taylor Coefficients ◽  
The Right ◽  
Arveson Space

Abstract In the Drury-Arveson space, we consider the subspace of functions whose Taylor coefficients are supported in a set Y⊂ ℕd with the property that ℕ\X + ej ⊂ ℕ\X for all j = 1, . . . , d. This is an easy example of shift-invariant subspace, which can be considered as a RKHS in is own right, with a kernel that can be explicitly calculated for specific choices of X. Every such a space can be seen as an intersection of kernels of Hankel operators with explicit symbols. Finally, this is the right space on which Drury’s inequality can be optimally adapted to a sub-family of the commuting and contractive operators originally considered by Drury.

scholarly journals On the Isomorphism Problem for Multiplier Algebras of Nevanlinna-Pick Spaces

2017 ◽  
Vol 69 (1) ◽  
pp. 54-106 ◽  
Author(s):  
Michael Hartz
Keyword(s):  
Hilbert Spaces ◽  
Special Class ◽  
Reproducing Kernel ◽  
Reproducing Kernels ◽  
Isomorphism Problem ◽  
Reproducing Kernel Hilbert Spaces ◽  
Universal Space ◽  
Kernel Hilbert Spaces ◽  
Arveson Space ◽  
Multiplier Algebras

AbstractWe continue the investigation of the isomorphism problem for multiplier algebras of reproducing kernel Hilbert spaces with the complete Nevanlinna-Pick property. In contrast to previous work in this area, we do not study these spaces by identifying them with the restrictions of a universal space, namely theDrury-Arveson space. Instead, we work directly with theHilbert spaces and their reproducing kernels. In particular, we show that two multiplier algebras of Nevanlinna-Pick spaces on the same set are equal if and only if the Hilbert spaces are equal. Most of the article is devoted to the study of a special class of complete Nevanlinna-Pick spaces on homogeneous varieties. We provide a complete answer to the question of when two multiplier algebras of spaces of this type are algebraically or isometrically isomorphic.This generalizes results of Davidson, Ramsey,Shalit, and the author.

scholarly journals Commutators and localization on the Drury–Arveson space

2011 ◽  
Vol 260 (3) ◽  
pp. 639-673 ◽  
Author(s):  
Quanlei Fang ◽  
Jingbo Xia
Keyword(s):  
Arveson Space

scholarly journals Row Contractions Annihilated by Interpolating Vanishing Ideals

2020 ◽  
Vol 2020 (20) ◽  
pp. 6597-6665
Author(s):  
Raphaël Clouâtre ◽  
Edward J Timko
Keyword(s):  
Multiplier Algebra ◽  
Interpolating Sequences ◽  
Several Variables ◽  
The Family ◽  
Direct Sum Decomposition ◽  
Nilpotent Matrices ◽  
Theoretic Characterization ◽  
Arveson Space ◽  
Vanishing Ideals

Abstract We study similarity classes of commuting row contractions annihilated by what we call higher-order vanishing ideals of interpolating sequences. Our main result exhibits a Jordan-type direct sum decomposition for these row contractions. We illustrate how the family of ideals to which our theorem applies is very rich, especially in several variables. We also give two applications of the main result. First, we obtain a purely operator theoretic characterization of interpolating sequences for the multiplier algebra of the Drury–Arveson space. Second, we classify certain classes of cyclic commuting row contractions up to quasi-similarity in terms of their annihilating ideals. This refines some of our recent work on the topic. We show how this classification is sharp: in general quasi-similarity cannot be improved to similarity. The obstruction to doing so is a scarcity of norm-controlled similarities between commuting tuples of nilpotent matrices, and we investigate this question in detail.

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