Residually finite-dimensional operator algebras

@article{Clouatre2018ResiduallyFO,
  title={Residually finite-dimensional operator algebras},
  author={Raphael Clouatre and Christopher Ramsey},
  journal={Journal of Functional Analysis},
  year={2018}
}
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10 Citations
Highly Influential Citations
2
Background Citations
5
Methods Citations
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10 Citations

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References

SHOWING 1-10 OF 53 REFERENCES

Residual finite dimensionality and representations of amenable operator algebras

Operator Spaces and Residually Finite-Dimensional C*-Algebras

Abstract For every operator space X the C *-algebra containing it in a universal way is residually finite-dimensional (that is, has a separating family of finite-dimensional representations). In…

Modules over Operator Algebras, and the Maximal C*-Dilation☆☆☆

Abstract We continue our study of the general theory of possibly nonselfadjoint algebras of operators on a Hilbert space, and modules over such algebras, developing a little more technology to…

OPERATOR ALGEBRAS OF FUNCTIONS

Crossed Products of Operator Algebras

We study crossed products of arbitrary operator algebras by locally compact groups of completely isometric automorphisms. We develop an abstract theory that allows for generalizations of many of the…

Elements of $C^{\ast }$ -algebras Attaining their Norm in a Finite-dimensional Representation

Abstract We characterize the class of RFD $C^{\ast }$ -algebras as those containing a dense subset of elements that attain their norm under a finite-dimensional representation. We show further that…

Noncommutative semialgebraic sets and associated lifting problems

We solve a class of lifting problems involving approximate polynomial relations (soft polynomial relations). Various associated C*-algebras are therefore projective. The technical lemma we need is a…

On residually finite-dimensional *-algebras

Exel and Loring have listed several conditions that are equivalent to the residual finite-dimensionality of a C*-algebra. We review and extend this list. A C*-algebra is said to be residually…

Operator algebras with contractive approximate identities, II

BOUNDARY REPRESENTATIONS FOR FAMILIES OF REPRESENTATIONS OF OPERATOR ALGEBRAS AND SPACES

In analogy with the peak points of the Shilov boundary of a uni- form algebra, Arveson defined the notion of boundary representations among the completely contractive representations of a unital…
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