Operator Spaces and Residually Finite-Dimensional C*-Algebras

Pestov, Vladimir

doi:10.1006/jfan.1994.1090

Cited by 37 publications

(11 citation statements)

References 17 publications

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“…Let M ⊂ B(H) be a subspace. We can associate to it a "free" C * -algebra C * M and a completely isometric linear map µ : M → C * M such that C * M = C * (µ(M)), and whenever ϕ : M → B(H ϕ ) is a completely contractive linear map, there is a unital * -homomorphism π ϕ : C * M → B(H ϕ ) with the property that π ϕ • µ = ϕ on M. Once again, C * M can be realized more concretely as the C *algebra generated by the image of M under an appropriate direct sum of completely contractive linear maps [36,Theorem 3.2].…”

Section: 1mentioning

confidence: 99%

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Residually finite-dimensional operator algebras

Clouâtre

Ramsey

2019

Journal of Functional Analysis

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We study non-selfadjoint operator algebras that can be entirely understood via their finite-dimensional representations. In contrast with the elementary matricial description of finite-dimensional C * -algebras, in the nonselfadjoint setting we show that an additional level of flexibility must be allowed. Motivated by this peculiarity, we consider a natural non-selfadjoint notion of residual finite-dimensionality. We identify sufficient conditions for the tensor algebra of a C * -correspondence to enjoy this property. To clarify the connection with the usual self-adjoint notion, we investigate the residual finite-dimensionality of the minimal and maximal C * -covers associated to an operator algebra.

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Section: 1mentioning

confidence: 99%

“…Acknowledgements. The first author wishes to thank Matt Kennedy for a stimulating discussion which brought [36] to his attention and sparked his interest in the residual finite-dimensionality of C * -covers.…”

Section: Introductionmentioning

confidence: 99%

Residually finite-dimensional operator algebras

Clouâtre

Ramsey

2019

Journal of Functional Analysis

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“…Pestov [17] once defined the universal C * -algebra of an operator space. Based on Pestov's idea on the universal C * -algebra of an operator space and the universal C * -algebra free product of C * -algebras (see ref.…”

Section: Introductionmentioning

confidence: 99%

Certain free products of operator spaces

Gao

2006

SCI CHINA SER A

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Certain free products are introduced for operator spaces and dual operator spaces. It is shown that the free product of operator spaces does not preserve the injectivity. The linking C * -algebra of the full free product of two ternary rings of operators (simply, TRO's) is *-isomorphic to the full free product of the linking C * -algebras of the two TRO's. The operator space-reduced free product of the preduals of von Neumann algebras agrees with the predual of the reduced free product of the von Neumann algebras. Each of two operator spaces can be embedded completely isometrically into the reduced free product of the operator spaces. Finally, an example is presented to show that the C * -algebra-reduced free product of two C * -algebras may be contractively isomorphic to a proper subspace of their reduced free product as operator spaces.

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“…Earlier, Choi [4] had shown that the full C* -algebra of the free group on two generators is RFD. The connections between freeness and the RFD property have been developed in [8,6,10]. In the course of this, Exel and Loring gave several equivalent conditions for the RFD property [6,Theorem 2.4].…”

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confidence: 99%

“…(iii) Pestov [10] has recently used the equivalence of (c) and (e). Spaces Rep(/1, H) have also been used recently in [1,9].…”

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confidence: 99%