Operator spaces with the WEP, the OLLP and the Gurarii property
Abstract
We construct non-exact operator spaces satisfying the Weak Expectation Property (WEP) and the Operator space version of the Local Lifting Property (OLLP). These examples should be compared with the example we recently gave of a -algebra with WEP and LLP. The construction produces several new analogues among operator spaces of the Gurarii space, extending Oikhberg's previous work. Each of our "Gurarii operator spaces" is associated to a class of finite dimensional operator spaces (with suitable properties). In each case we show the space exists and is unique up to completely isometric isomorphism.
Keywords
Cite
@article{arxiv.2104.05008,
title = {Operator spaces with the WEP, the OLLP and the Gurarii property},
author = {Gilles Pisier},
journal= {arXiv preprint arXiv:2104.05008},
year = {2026}
}
Comments
Minor changes mainly to clarify or add more details to certain proofs. Added reference to Pedersen in 2023. minor improvements in january 2026. Paper to appear in Annales Fennici Mathematici