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EMBEDDINGS AND $C^{\ast }$-ENVELOPES OF EXACT OPERATOR SYSTEMS

Part of: Linear spaces and algebras of operators Selfadjoint operator algebras

Published online by Cambridge University Press:  02 May 2017

PREETI LUTHRA  and
AJAY KUMAR Open the ORCID record for AJAY KUMAR [Opens in a new window]
PREETI LUTHRA
Affiliation:
Department of Mathematics, University of Delhi, Delhi-110007, India email [email protected]
AJAY KUMAR*
Affiliation:
Department of Mathematics, University of Delhi, Delhi-110007, India email [email protected]
*
✉[email protected]
Rights & Permissions [Opens in a new window]

Abstract

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We prove a necessary and sufficient condition for embeddability of an operator system into ${\mathcal{O}}_{2}$. Using Kirchberg’s theorems on a tensor product of ${\mathcal{O}}_{2}$ and ${\mathcal{O}}_{\infty }$, we establish results on their operator system counterparts ${\mathcal{S}}_{2}$ and ${\mathcal{S}}_{\infty }$. Applications of the results, including some examples describing $C^{\ast }$-envelopes of operator systems, are also discussed.

Keywords

operator systemsexactnessC∗ -envelopesCuntz algebrastensor products

MSC classification

Primary: 46L06: Tensor products of $C^*$-algebras
Secondary: 46L05: General theory of $C^*$-algebras 46L07: Operator spaces and completely bounded maps 47L25: Operator spaces (= matricially normed spaces)
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 96 , Issue 2 , October 2017 , pp. 274 - 285
Copyright
© 2017 Australian Mathematical Publishing Association Inc. 

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