## Illinois Journal of Mathematics

### The {OLLP} and $\scr T$-local reflexivity of operator spaces

Z. Dong

#### Abstract

In this paper, we study two `dual' problems in the operator space theory. We first show that if $L$ is a finite-dimensional operator space, then $L$ has the OLLP if and only if for any indexed family of operator spaces $(W_{i})_{i\in I}$ and a free ultrafilter $\mathcal{U}$ on $I$, we have a complete isometry $\prod(L\ha W_{i})/\mathcal{U}=L\ha\prod W_{i}/\mathcal{U}.$ Next, we show that if $W$ is an operator space, then $(T_{n}\ck W )^{**}=T_{n}\ck W^{**}$ holds if and only if $W$ is $\mathcal{T}$-locally reflexive, if and only if for any finitely representable operator spaces $V$, we have an isometry $\mathcal{I}(V, W^{*})=(V\ck W)^{*}$.

#### Article information

Source
Illinois J. Math., Volume 51, Number 4 (2007), 1103-1122.

Dates
First available in Project Euclid: 13 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1258138535

Digital Object Identifier
doi:10.1215/ijm/1258138535

Mathematical Reviews number (MathSciNet)
MR2417418

Zentralblatt MATH identifier
1155.46025

#### Citation

Dong, Z. The {OLLP} and $\scr T$-local reflexivity of operator spaces. Illinois J. Math. 51 (2007), no. 4, 1103--1122. doi:10.1215/ijm/1258138535. https://projecteuclid.org/euclid.ijm/1258138535