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- W1883893351 abstract "We realize the noncommutative Gurarij space $mathbb{NG}$ defined by Oikhberg as the Fraisse limit of the class of finite-dimensional $1$-exact operator spaces. As a consequence we deduce that the concommutative Gurarij space is unique up to completely isometric isomorphism, homogeneous, and universal among separable $1$-exact operator spaces. We also prove that $mathbb{NG}$ is the unique separable nuclear operator space with the property that the canonical triple morphism from the universal TRO to the triple envelope is an isomorphism. We deduce from this fact that $mathbb{NG}$ does not embed completely isometrically into an exact C*-algebra, and it is not completely isometrically isomorphic to a C*-algebra or to a TRO. We also provide a canonical construction of $mathbb{NG}$, which shows that the group of surjective complete isometries of $mathbb{NG}$ is universal among Polish groups. Analog results are proved in the commutative setting and, more generally, for $M_{n}$-spaces. In particular, we provide a new characterization and canonical construction of the Gurarij Banach space." @default.
- W1883893351 created "2016-06-24" @default.
- W1883893351 creator A5007326745 @default.
- W1883893351 date "2014-10-13" @default.
- W1883893351 modified "2023-09-23" @default.
- W1883893351 title "Uniqueness, universality, and homogeneity of the noncommutative Gurarij space" @default.
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