## 18 Citations

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 $\mathbb{C}^d$.…

A multiplier algebra functional calculus

- MathematicsTransactions of the American Mathematical Society
- 2018

This paper generalizes the classical Sz.-Nagy--Foias $H^{\infty}(\mathbb{D})$ functional calculus for Hilbert space contractions. In particular, we replace the single contraction $T$ with a tuple…

Multiplier tests and subhomogeneity of multiplier algebras

- Mathematics
- 2020

Multipliers of reproducing kernel Hilbert spaces can be characterized in terms of positivity of $n \times n$ matrices analogous to the classical Pick matrix. We study for which reproducing kernel…

Ideals in a multiplier algebra on the ball

- Mathematics
- 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,…

Gelfand transforms and boundary representations of complete Nevanlinna–Pick quotients

- MathematicsTransactions of the American Mathematical Society
- 2020

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…

Analytic functionals for the non-commutative disc algebra

- MathematicsJournal of Functional Analysis
- 2021

Multiplier algebras of complete Nevanlinna–Pick spaces: Dilations, boundary representations and hyperrigidity

- Mathematics
- 2016

Totally null sets and capacity in Dirichlet type spaces

- MathematicsJournal of the London Mathematical Society
- 2022

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

A completely bounded non-commutative Choquet boundary for operator spaces

- Mathematics
- 2017

We develop a completely bounded counterpart to the non-commutative Choquet boundary of an operator space. We show how the class of completely bounded linear maps is too large to accommodate our…

Non-commutative measure theory: Henkin and analytic functionals on $$\mathrm {C}^*$$-algebras

- MathematicsMathematische Annalen
- 2022

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…

## References

SHOWING 1-10 OF 61 REFERENCES

Noncommutative interpolation and Poisson transforms

- Mathematics
- 1997

General results of interpolation (e.g., Nevanlinna-Pick) by elements in the noncommutative analytic Toeplitz algebraF∞ (resp., noncommutative disc algebraAn) with consequences to the interpolation by…

Ideals in a multiplier algebra on the ball

- Mathematics
- 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,…

A non-self-adjoint Lebesgue decomposition

- Mathematics
- 2013

We study the structure of bounded linear functionals on a class of non-self-adjoint operator algebras that includes the multiplier algebra of every complete Nevanlinna-Pick space, and in particular…

Factorization and reflexivity on Fock spaces

- Mathematics
- 1994

AbstractThe framework of the paper is that of the full Fock space
$$\mathcal{F}^2 (\mathcal{H}_n )$$
and the Banach algebraF∞ which can be viewed as non-commutative analogues of the Hardy spacesH2…

Operator Theory and Function Theory in Drury–Arveson Space and Its Quotients

- Mathematics
- 2013

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…

Multipliers and essential norm on the Drury-Arveson space

- Mathematics
- 2010

It is well known that for multipliers f of the Drury-Arveson space H 2 n , ∥f∥ ∞ does not dominate the operator norm of M f . We show that in general ∥f∥ ∞ does not even dominate the essential norm…

The algebraic structure of non-commutative analytic Toeplitz algebras

- Mathematics
- 1998

The non-commutative analytic Toeplitz algebra is the wot– closed algebra generated by the left regular representation of the free semigroup on n generators. We develop a detailed picture of the…

Operator algebras for analytic varieties

- Mathematics
- 2012

We study the isomorphism problem for the multiplier algebras of irreducible complete Pick kernels. These are precisely the restrictionsMV of the multiplier algebraM of Drury-Arveson space to a…

Nevanlinna-Pick interpolation for non-commutative analytic Toeplitz algebras

- Mathematics
- 1998

The non-commutative analytic Toeplitz algebra is the WOT-closed algebra generated by the left regular representation of the free semigroup onn generators. We obtain a distance formula to an arbitrary…

Poisson Transforms on Some C*-Algebras Generated by Isometries

- Mathematics
- 1999

Abstract A noncommutative Poisson transform associated to a certain class of sequences of operators on Hilbert spaces, with property (P), is defined on some universal C *-algebras (resp.…