This is an announcement for the paper "Uniqueness, universality, and homogeneity of the noncommutative Gurarij space" by Martino Lupini.

Abstract: We realize the noncommutative Gurarij space $\mathbb{NG}$ defined by Oikhberg as the Fra"{\i}ss'{e} limit of the class of finite-dimensional $1$-exact operator spaces. As a consequence we deduce that the noncommutative Gurarij space is unique up to completely isometric isomorphism, homogeneous, and universal among separable $1$-exact operator spaces. Moreover we show that $\mathbb{NG}$ is isometrically isomorphic to the Gurarij Banach space. Therefore $\mathbb{NG}$ can be thought as a canonical operator space structure on the Gurarij Banach space.

Archive classification: math.FA math.LO

Mathematics Subject Classification: 46L07 (Primary) 03C30 (Secondary)

Remarks: 24 pages

Submitted from: mlupini@yorku.ca

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1410.3345

or

http://arXiv.org/abs/1410.3345