An abstract characterization of unital operator spaces
| dc.creator | Huang, Xu-Jian | |
| dc.creator | Ng, Chi-Keung | |
| dc.date | 2008-05-16 | |
| dc.date | 2008-05-27 | |
| dc.date.accessioned | 2026-07-07T09:40:47Z | |
| dc.date.available | 2026-07-07T09:40:47Z | |
| dc.description | In this article, we give an abstract characterization of the ``identity'' of an operator space $V$ by looking at a quantity $n_{cb}(V,u)$ which is defined in analogue to a well-known quantity in Banach space theory. More precisely, we show that there exists a complete isometry from $V$ to some $\mathcal{L}(H)$ sending $u$ to ${\rm id}_H$ if and only if $n_{cb}(V,u) =1$. We will use it to give an abstract characterization of operator systems. Moreover, we will show that if $V$ is a unital operator space and $W$ is a proper complete $M$-ideal, then $V/W$ is also a unital operator space. As a consequece, the quotient of an operator system by a proper complete $M$-ideal is again an operator system. In the appendix, we will also give an abstract characterisation of ``non-unital operator systems'' using an idea arose from the definition of $n_{cb}(V,u)$. | |
| dc.description | Some remarks were added | |
| dc.identifier | https://arxiv.org/abs/0805.2447 | |
| dc.identifier | http://arxiv.org/abs/0805.2447 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/161596 | |
| dc.subject | Operator Algebras | |
| dc.subject | Functional Analysis | |
| dc.title | An abstract characterization of unital operator spaces | |
| dc.type | text |