Guarded Fraïssé Banach spaces

2024/08/22 by Marek Cúth, Cúth, Marek, Noé de Rancourt +3
Mathematics · #Advanced Banach Space Theory

paper · pdf · doi:10.48550/arxiv.2408.12755

Abstract

We characterize separable Banach spaces having G_δ isometry classes in the Polish codings P, P_∞ and B introduced by Cúth-Doležal-Doucha-Kurka [13] as those being guarded Fraïssé, a weakening of the notion of Fraïssé Banach spaces defined by Ferenczi-Lopez-Abad-Mbombo-Todorcevic [18]. We prove a Fraïssé correspondence for those spaces and make links with the notion of ω-categoricity from continuous logic, showing that ω-categorical Banach spaces are a natural source of guarded Fraïssé Banach spaces. Using those results, we prove that for many values of (p, q), the Banach space L_p(L_q) has a G_δ isometry class; we precisely characterize those values.

Related

• Polish spaces of Banach spaces. Complexity of isometry and isomorphism classes
• Almost Fraïssé Banach spaces
• Envelopes in Banach spaces
• Displaying Polish groups on separable Banach spaces
• Tightness of Banach spaces and Baire category