2014/10/13 by Martino Lupini, Lupini, Martino
Mathematics · #03C30 (Secondary) #46L07 (Primary) #Advanced Banach Space Theory #Advanced Operator Algebra Research #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Logic (math.LO) #Operator Algebras (math.OA)
paper · pdf · doi:10.48550/arxiv.1410.3345
openalex publication_date 2014/10/13 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28
We realize the noncommutative Gurarij space mathbbNG defined by Oikhberg\nas the Fra " iss 'e limit of the class of finite-dimensional 1-exact\noperator spaces. As a consequence we deduce that the concommutative Gurarij\nspace is unique up to completely isometric isomorphism, homogeneous, and\nuniversal among separable 1-exact operator spaces. We also prove that\n mathbbNG is the unique separable nuclear operator space with the property\nthat the canonical triple morphism from the universal TRO to the triple\nenvelope is an isomorphism. We deduce from this fact that mathbbNG does\nnot embed completely isometrically into an exact C*-algebra, and it is not\ncompletely isometrically isomorphic to a C*-algebra or to a TRO. We also\nprovide a canonical construction of mathbbNG, which shows that the group\nof surjective complete isometries of mathbbNG is universal among Polish\ngroups. Analog results are proved in the commutative setting and, more\ngenerally, for Mn-spaces. In particular, we provide a new characterization\nand canonical construction of the Gurarij Banach space.\n