Gurarii operators are generic

2021/12/04 by Banakh, Taras, Garbulińska-Wȩgrzyn, Joanna
#46B04 #46B28 #47A05 #47A65 #54B52 #54H05 #54H15 #FOS: Mathematics #Functional Analysis (math.FA) #General Topology (math.GN)

paper · doi:10.48550/arxiv.2112.02283

Abstract

Answering a question of Garbulińska-Wȩgrzyn and Kubiś, we prove that Gurarii operators form a dense G_δ-set in the space \mathcal B(\mathbb G) of all nonexpansive operators on the Gurarii space \mathbb G, endowed with the strong operator topology. This implies that the set of universal operators on \mathbb G form a residual set in \mathcal B(\mathbb G).

Related

• Operator spaces with the WEP, the OLLP and the Gurarii property
• Uniqueness, universality, and homogeneity of the noncommutative Gurarij\n space
• On Wolfgang Lusky's paper "The Gurarij spaces are unique''
• A universal nuclear operator system
• Model-theoretic aspects of the Gurarij operator system