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ORDER EMBEDDING OF A MATRIX ORDERED SPACE

Part of: Selfadjoint operator algebras

Published online by Cambridge University Press:  21 June 2011

ANIL K. KARN
ANIL K. KARN*
Affiliation:
Department of Mathematics, Deen Dayal Upadhyaya College, University of Delhi, Karam Pura, New Delhi 110 015, India (email: anil.karn@gmail.com)
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Abstract

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We characterize certain properties in a matrix ordered space in order to embed it in a C*-algebra. Let such spaces be called C*-ordered operator spaces. We show that for every self-adjoint operator space there exists a matrix order (on it) to make it a C*-ordered operator space. However, the operator space dual of a (nontrivial) C*-ordered operator space cannot be embedded in any C*-algebra.

Keywords

matrix ordered spaceoperator spaceoperator systemL∞-matricially Riesz normed spaceC*-ordered operator spaceC*-matricially Riesz normed space

MSC classification

Secondary: 46L07: Operator spaces and completely bounded maps
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 84 , Issue 1 , August 2011 , pp. 10 - 18
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

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