An abstract characterization of unital operator spaces

Details An abstract characterization of unital operator spaces An abstract characterization of unital operator spaces

2008-05-16

arxiv.org/abs/0805.2447v2

Mathematics

Operator Algebras

Some remarks were added

Scientific paper

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 $n_{cb}(V,u)$.

Affiliated with

Also associated with

No associations

Rating

An abstract characterization of unital operator spaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with An abstract characterization of unital operator spaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and An abstract characterization of unital operator spaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-272387