# Row Contractions Annihilated by Interpolating Vanishing Ideals

@article{Clouatre2019RowCA, title={Row Contractions Annihilated by Interpolating Vanishing Ideals}, author={Raphael Clouatre and Edward J. Timko}, journal={International Mathematics Research Notices}, year={2019} }

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…

## 2 Citations

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A unitarily invariant, complete Nevanlinna--Pick kernel $K$ on the unit ball determines a class of operators on Hilbert space called $K$-contractions. We study those $K$-contractions that are…

### 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…

## References

SHOWING 1-10 OF 40 REFERENCES

### 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…

### Unitary Equivalence and Similarity to Jordan Models for Weak Contractions of Class C0

- MathematicsCanadian Journal of Mathematics
- 2015

Abstract We obtain results on the unitary equivalence of weak contractions of class ${{C}_{0}}$ to their Jordan models under an assumption on their commutants. In particular, our work addresses the…

### Isometric dilations for infinite sequences of noncommuting operators

- Mathematics
- 1989

This paper develops a dilation theory for {T,}n=l an infinite sequence of noncommuting operators on a Hilbert space, when the matrix [T1, T2, ... ] is a contraction. A Wold decomposition for an…

### Invariant Subspaces and Nevanlinna–Pick Kernels

- Mathematics
- 2000

Abstract A theorem of Beurling–Lax–Halmos represents a subspace M of H2 C ( D )—the Hardy space of analytic functions with values in the Hilbert space E and square summable power series—invariant for…

### Similarity Results for Operators of Class C0

- Mathematics
- 2011

If T is a multiplicity-free contraction of class C0 with minimal function mT, then it is quasisimilar to the Jordan block S(mT). In case mT is a Blaschke product with simple roots forming a Carleson…

### Interpolation and Commutant Lifting for Multipliers on Reproducing Kernel Hilbert Spaces

- Mathematics
- 2001

We obtain an explicit representation formula and a Nevanlinna-Pick-type interpolation theorem for the multiplier space of the reproducing kernel space ℌ(k d ) of analytic functions on the…

### Interpolating sequences in spaces with the complete Pick property

- Mathematics
- 2017

We characterize interpolating sequences for multiplier algebras of spaces with the complete Pick property. Specifically, we show that a sequence is interpolating if and only if it is separated and…