The isomorphism problem for some universal operator algebras

@article{Davidson2010TheIP,
  title={The isomorphism problem for some universal operator algebras},
  author={Kenneth R. Davidson and Christopher Ramsey and Orr Moshe Shalit},
  journal={Advances in Mathematics},
  year={2010},
  volume={228},
  pages={167-218}
}
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References

SHOWING 1-10 OF 48 REFERENCES

The algebraic structure of non-commutative analytic Toeplitz algebras

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…

The structure of free semigroup algebras

A free semigroup algebra is the wot-closed algebra generated by an n-tuple of isometries with pairwise orthogonal ranges. The interest in these algebras arises primarily from two of their interesting…

Quotients of standard Hilbert modules

We initiate a study of Hilbert modules over the polynomial algebra that are obtained by completing with respect to an inner product having certain natural properties. A standard Hilbert module is a…

A LARGE WEAK OPERATOR CLOSURE FOR THE ALGEBRA GENERATED BY TWO ISOMETRIES

Given two (or n) isometries on a Hilbert space H, such that their ranges are mutually orthogonal, one can use them to generate a C ⁄ -algebra. If the ranges sum to H, then this C ⁄ -algebra, the…

Essentially normal Hilbert modules and K-homology

This paper mainly concerns the essential normality of graded submodules. Essentially all of the basic Hilbert modules that have received attention over the years are p-essentially normal—including…

Stable polynomial division and essential normality of graded Hilbert modules

It is shown that when the algebra of polynomials in $d$ variables is given the natural $\ell^1$ norm, then every ideal is linearly equivalent to an ideal that has the stable division property.

Nevanlinna–Pick Interpolation and Factorization of Linear Functionals

If $${\mathfrak{A}}$$ is a unital weak-* closed algebra of multiplication operators on a reproducing kernel Hilbert space which has the property $${\mathbb{A}_1(1)}$$, then the cyclic invariant…

Tensor Algebras overC*-Correspondences: Representations, Dilations, andC*-Envelopes☆

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Invariant Subspaces and Hyper‐Reflexivity for Free Semigroup Algebras

A free semigroup algebra is the weak operator topology closed algebra generated by a set of isometries with pairwise orthogonal ranges. The most important example is the left regular free semigroup…

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