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Banach spaces of bounded Szlenk index

Tom 183 / 2007

Studia Mathematica 183 (2007), 63-97 MSC: 46B20, 54H05. DOI: 10.4064/sm183-1-4

Streszczenie

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

Autorzy

• E. OdellDepartment of Mathematics
The University of Texas
1 University Station C1200
Austin, TX 78712, U.S.A.
e-mail
• Th. SchlumprechtDepartment of Mathematics
Texas A&M University
College Station, TX 78712, U.S.A.
e-mail
• A. ZsákSchool of Mathematical Sciences
University of Nottingham
University Park
Nottingham NG7 2RD, United Kingdom
e-mail

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