Banach spaces of bounded Szlenk index

• Autorzy: E. Odell , Th. Schlumprecht , A. Zsák
• Języki publikacji: EN

Abstrakty

EN

For a countable ordinal α we denote by $𝓒_{α}$ the class of separable, reflexive Banach spaces whose Szlenk index and the Szlenk index of their dual are bounded by α. We show that each $𝓒_{α}$ admits a separable, reflexive universal space. We also show that spaces in the class $𝓒_{ω^{α·ω}}$ embed into spaces of the same class with a basis. As a consequence we deduce that each $𝓒_{α}$ is analytic in the Effros-Borel structure of subspaces of C[0,1].

Kategorie tematyczne

• 54H05: Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)
• 46B20: Geometry and structure of normed linear spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2007
• Tom: 183
• Numer: 1
• Strony: 63-97

Daty

wydano

2007

Twórcy

autor

E. Odell

• Department of Mathematics, The University of Texas, 1 University Station C1200, Austin, TX 78712, U.S.A.

autor

Th. Schlumprecht

• Department of Mathematics, Texas A&M University, College Station, TX 78712, U.S.A.

autor

A. Zsák

• School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom

Identyfikatory

DOI

10.4064/sm183-1-4