Non-universal families of separable Banach spaces

• Autorzy: Ondřej Kurka
• Języki publikacji: EN

Abstrakty

EN

We prove that if 𝓒 is a family of separable Banach spaces which is analytic with respect to the Effros Borel structure and no X ∈ 𝓒 is isometrically universal for all separable Banach spaces, then there exists a separable Banach space with a monotone Schauder basis which is isometrically universal for 𝓒 but not for all separable Banach spaces. We also establish an analogous result for the class of strictly convex spaces.

Kategorie tematyczne

• 54H05: Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)
• 46B20: Geometry and structure of normed linear spaces
• 46B04: Isometric theory of Banach spaces
• 46B15: Summability and bases
• 46B25: Classical Banach spaces in the general theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2016
• Tom: 233
• Numer: 2
• Strony: 153-168

Daty

wydano

2016

Twórcy

autor

Ondřej Kurka

• Department of Mathematical Analysis, Charles University, Sokolovská 83, 186 75 Praha 8, Czech Republic

Identyfikatory

DOI

10.4064/sm8380-4-2016