ORDER EMBEDDING OF A MATRIX ORDERED SPACE

Authors

  • anil karn

Keywords:

Matrix ordered space, operator space, operator system, $L^{\infty}$-matricially Riesz normed space, $C^{\ast}$-ordered operator space, $C^{\ast}$-matricially Riesz normed space.

Abstract

We characterize certain properties in a matrix ordered space in order to order embed it in a $C^{\ast}$-algebra. Let such spaces be called $C^{\ast}$-ordered operator spaces. We show that for every self-adjoint operator space there exists a matrix order (on it) to make it a $C^{\ast}$-ordered operator space. However, the operator space dual of a (non-trivial) $C^{\ast}$-ordered operator space can not be embedded in any $C^{\ast}$-algebra.

Published

2011-10-19

Issue

Vol. 84 No. 1 (2011)

Section

Articles
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