Bilinear forms on exact operator spaces and B(H)\otimes B(H)

Details Bilinear forms on exact operator spaces and B(H)\otimes B(H) Bilinear forms on exact operator spaces and B(H)\otimes B(H)

1993-08-24

arxiv.org/abs/math/9308208v1

Geometric and Functional Analysis (GAFA Journal) 5 (1995) 329-363.

Mathematics

Functional Analysis

Scientific paper

Let $E,F$ be exact operators (For example subspaces of the $C^*$-algebra $K(H)$ of all the compact operators on an infinite dimensional Hilbert space $H$). We study a class of bounded linear maps $u\colon E\to F^*$ which we call tracially bounded. In particular, we prove that every completely bounded (in short $c.b.$) map $u\colon E\to F^*$ factors boundedly through a Hilbert space. This is used to show that the set $OS_n$ of all $n$-dimensional operator spaces equipped with the $c.b.$ version of the Banach Mazur distance is not separable if $n>2$. As an application we show that there is more than one $C^*$-norm on $B(H)\otimes B(H)$, or equivalently that $$B(H)\otimes_{\min}B(H)\not=B(H)\otimes_{\max}B(H),$$ which answers a long standing open question. Finally we show that every ``maximal" operator space (in the sense of Paulsen) is not exact in the infinite dimensional case, and in the finite dimensional case, we give a lower bound for the ``exactness constant".

Affiliated with

Also associated with

No associations

Rating

Bilinear forms on exact operator spaces and B(H)\otimes B(H) 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 Bilinear forms on exact operator spaces and B(H)\otimes B(H), we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Bilinear forms on exact operator spaces and B(H)\otimes B(H) will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-126907