Corpus ID: 233209853

Operator spaces with the WEP, the OLLP and the Gurarii property

@inproceedings{Pisier2021OperatorSW,
  title={Operator spaces with the WEP, the OLLP and the Gurarii property},
  author={Gilles Pisier},
  year={2021}
}
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 C∗-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… Expand

References

SHOWING 1-10 OF 48 REFERENCES
Commutants of unitaries in UHF algebras and functorial properties of exactness.
Since Grothendieck showed in [18] that the theory of tensor products of locally convex spaces gives important informations on functional analytic properties of locally convex vector spaces, it wasExpand
uniqueness
This document proves that a cycloid (as opposed to some other shape such as a parabola) is the unique analytic solution to the brachistochrone problem. Define Tcyc(x,y) to be the time to get fromExpand
Fraïssé limits in functional analysis
  • M. Lupini
  • Mathematics
  • Advances in Mathematics
  • 2018
We provide a unified approach to Fra\"isse limits in functional analysis, including the Gurarij space, the Poulsen simplex, and their noncommutative analogs. We obtain in this general framework manyExpand
A proof of uniqueness of the Gurariĭ space
We present a short and elementary proof of isometric uniqueness of the Gurariĭ space.
The non-commutative Gurarii space
Abstract.We construct a “universal space” for 1-exact finite dimensional operator spaces (an analogue of the Gurarii space).
On the lifting property for universal C∗-algebras of operator spaces
  • J. Operator Theory 46
  • 2001
FraïSSé Limits of Metric Structures
The Gurarij spaces are unique
Bilinear forms on exact operator spaces andB(H)⊗B(H)
AbstractLetE, F be exact operator spaces (for example subspaces of theC*-algebraK(H) of all the compact operators on an infinite dimensional Hilbert spaceH). We study a class of bounded linear mapsu:Expand
A non-nuclear $$C^*$$-algebra with the weak expectation property and the local lifting property
  • G. Pisier
  • Mathematics
  • Inventiones mathematicae
  • 2020
We construct the first example of a $C^*$-algebra $A$ with the properties in the title. This gives a new example of non-nuclear $A$ for which there is a unique $C^*$-norm on $A \otimes A^{op}$. ThisExpand
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