Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-05T21:09:18.505Z Has data issue: false hasContentIssue false

ORDER EMBEDDING OF A MATRIX ORDERED SPACE

Published online by Cambridge University Press:  21 June 2011

ANIL K. KARN*
Affiliation:
Department of Mathematics, Deen Dayal Upadhyaya College, University of Delhi, Karam Pura, New Delhi 110 015, India (email: [email protected])
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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.

Type
Research Article
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

References

[1]Blecher, D. P. and Neal, M., ‘Open partial isometries and positivity in operator spaces’, Studia Math. 182 (2007), 227262.CrossRefGoogle Scholar
[2]Choi, M. D. and Effros, E. G., ‘Injectivity and operator spaces’, J. Funct. Anal. 24 (1977), 156209.CrossRefGoogle Scholar
[3]Effros, E. G. and Ruan, Z. J., ‘On the abstract characterization of operator spaces’, Proc. Amer. Math. Soc. 119 (1993), 579584.CrossRefGoogle Scholar
[4]Jameson, G. J. O., Ordered Linear Spaces, Lecture Notes in Mathematics, 141 (Springer, New York, 1970).CrossRefGoogle Scholar
[5]Kadison, R. and Ringrose, J., Fundamentals of the Theories of Operator Algebras, I (Academic Press, New York, 1983).Google Scholar
[6]Karn, A. K., ‘A p-theory of ordered normed spaces’, Positivity 14 (2010), 441458.CrossRefGoogle Scholar
[7]Karn, A. K. and Vasudevan, R., ‘Approximate matrix order unit spaces’, Yokohama Math. J. 44 (1997), 7391.Google Scholar
[8]Karn, A. K. and Vasudevan, R., ‘Matrix duality for matrix ordered spaces’, Yokohama Math. J. 45 (1998), 118.Google Scholar
[9]Karn, A. K. and Vasudevan, R., ‘Characterizations of matricially Riesz normed spaces’, Yokohama Math. J. 47 (2000), 143153.Google Scholar
[10]Ruan, Z. J., ‘Subspaces of C *-algebras’, J. Funct. Anal. 76 (1988), 217230.CrossRefGoogle Scholar
[11]Schreiner, W. J., ‘Matrix regular operator spaces’, J. Funct. Anal. 152 (1998), 136175.CrossRefGoogle Scholar
[12]Werner, W., ‘Subspaces of L(H) that are *-invariant’, J. Funct. Anal. 193 (2002), 207223.CrossRefGoogle Scholar