# Ideals in a multiplier algebra on the ball

@article{Clouatre2015IdealsIA, title={Ideals in a multiplier algebra on the ball}, author={Raphael Clouatre and Kenneth R. Davidson}, journal={arXiv: Operator Algebras}, year={2015} }

We study the ideals of the closure of the polynomial multipliers on the Drury-Arveson space. Structural results are obtained by investigating the relation between an ideal and its weak-$*$ closure, much in the spirit of the corresponding classical facts for the disc algebra. Zero sets for multipliers are also considered and are deeply intertwined with the structure of ideals. Our approach is primarily based on duality arguments.

## 10 Citations

### Cyclicity in the Drury-Arveson space and other weighted Besov spaces

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. Let H be a space of analytic functions on the unit ball B d in C d with multiplier algebra Mult( H ) . A function f ∈ H is called cyclic if the set [ f ] , the closure of { ϕf : ϕ ∈ Mult( H ) } ,…

### Gelfand transforms and boundary representations of complete Nevanlinna–Pick quotients

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The main objects under study are quotients of multiplier algebras of certain complete Nevanlinna--Pick spaces, examples of which include the Drury--Arveson space on the ball and the Dirichlet space…

### Totally null sets and capacity in Dirichlet type spaces

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In the context of Dirichlet type spaces on the unit ball of Cd$\mathbb {C}^d$ , also known as Hardy–Sobolev or Besov–Sobolev spaces, we compare two notions of smallness for compact subsets of the…

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Henkin functionals on non-commutative C-algebras have recently emerged as a pivotal link between operator theory and complex function theory in several variables. Our aim in this paper is…

### Multipliers of Drury–Arveson Space: A Survey

- MathematicsInterpolation and Realization Theory with Applications to Control Theory
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The Drury–Arveson Space, as a Hilbert function space, plays an important role in multivariable operator theory. We give a brief survey of some aspects of the multipliers on the space.

### A noncommutative Bishop peak interpolation-set theorem

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. We prove a noncommutative version of Bishop’s peak interpolation-set theorem.

### Analytical Aspects of the Drury-Arveson Space

- MathematicsHandbook of Analytic Operator Theory
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We give a brief review of the Drury-Arveson space and its associated operator theory. We then survey those recent results on that space where analytical methods play a predominant role. A number of…

### Interpolation and duality in algebras of multipliers on the ball

- Mathematics
- 2020

We study the multiplier algebras $A(\mathcal{H})$ obtained as the closure of the polynomials on certain reproducing kernel Hilbert spaces $\mathcal{H}$ on the ball $\mathbb{B}_d$ of $\mathbb{C}^d$.…

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