Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-28T15:47:34.016Z Has data issue: false hasContentIssue false
  • English
  • Français

QUOTIENT AND PSEUDO UNIT IN NONUNITAL OPERATOR SYSTEM

Part of: Selfadjoint operator algebras

Published online by Cambridge University Press:  02 April 2015

LI LIU  and
JIAN-ZE LI
LI LIU
Affiliation:
Grenoble University, Laboratoire Jean Kuntzmann, BP 53, 38 041 Grenoble Cedex 9, France email [email protected]
JIAN-ZE LI*
Affiliation:
Department of Mathematics, Tianjin University, Tianjin 300072, PR China email [email protected]
*
✉[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 define the quotient and complete NUOS-quotient map (NUOS stands for nonunital operator system) in the category of nonunital operator systems. We prove that the greatest reduced tensor product max0 is projective in some sense. Moreover, we define a pseudo unit in a nonunital operator system and give some necessary and sufficient conditions under which a nonunital operator system has an operator system structure.

Keywords

nonunital operator systemcomplete NUOS-quotient mappseudo unit

MSC classification

Primary: 46L06: Tensor products of $C^*$-algebras
Secondary: 46L07: Operator spaces and completely bounded maps
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 92 , Issue 1 , August 2015 , pp. 123 - 132
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

References

Effros, E. G. and Ruan, Z.-J., Operator Spaces, London Mathematical Society Monographs, 23 (Clarendon Press, Oxford, 2000).Google Scholar
Han, K. H., ‘On maximal tensor products and quotient maps of operator systems’, J. Math. Anal. Appl. 384 (2011), 375–386.CrossRefGoogle Scholar
Han, K. H. and Paulsen, V. I., ‘An approximation theorem for nuclear operator systems’, J. Funct. Anal. 261 (2011), 999–1009.CrossRefGoogle Scholar
Huang, X. J. and Ng, C. K., ‘An abstract characterisation of unital operator spaces’, J. Operator Theory 67 (2012), 289–298.Google Scholar
Kavruk, A. S., Paulsen, V. I., Todorov, I. G. and Tomforde, A. M., ‘Tensor products of operator systems’, J. Funct. Anal. 261 (2011), 267–299.CrossRefGoogle Scholar
Kavruk, A. S., Paulsen, V. I., Todorov, I. G. and Tomforde, A. M., ‘Quotients, exactness and nuclearity in the operator system category’, Adv. Math. 235 (2013), 321–360.CrossRefGoogle Scholar
Li, J. Z. and Ng, C. K., ‘Tensor products for nonunital operator systems’, J. Math. Anal. Appl. 396(2) (2012), 601–605.CrossRefGoogle Scholar
Ng, C. K., ‘Operator subspaces of L(H) with induced matrix orderings’, Indiana Univ. Math. J. 60 (2011), 577–610.CrossRefGoogle Scholar
Paulsen, V. I., Completely Bounded Maps and Operator Algebras, Cambridge Studies in Advanced Mathematics, 78 (Cambridge University Press, Cambridge, 2002).Google Scholar
Paulsen, V. I., Todorov, I. G. and Tomforde, A. M., ‘Operator system structures on ordered spaces’, Proc. Lond. Math. Soc. (3) 102 (2011), 25–49.CrossRefGoogle Scholar
Paulsen, V. I. and Tomforde, A. M., ‘Vector spaces with an order unit’, Indiana Univ. Math. J. 58 (2009), 1319–1359.CrossRefGoogle Scholar
Werner, W., ‘Subspaces of L(H) that are ∗-invariant’, J. Funct. Anal. 193 (2002), 207–223.CrossRefGoogle Scholar
Werner, W., ‘Multipliers on matrix ordered operator spaces and some K-groups’, J. Funct. Anal. 206 (2004), 356–378.CrossRefGoogle Scholar