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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 liliu.math@gmail.com
JIAN-ZE LI*
Affiliation:
Department of Mathematics, Tianjin University, Tianjin 300072, PR China email lijianze@tju.edu.cn
*
✉lijianze@tju.edu.cn
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Abstract

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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. 

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