Minimality properties of Tsirelson type spaces

• Autorzy: Denka Kutzarova , Denny H. Leung , Antonis Manoussakis , Wee-Kee Tang
• Języki publikacji: EN

Abstrakty

EN

We study minimality properties of partly modified mixed Tsirelson spaces. A Banach space with a normalized basis $(e_{k})$ is said to be subsequentially minimal if for every normalized block basis $(x_{k})$ of $(e_{k})$, there is a further block basis $(y_{k})$ of $(x_{k})$ such that $(y_{k})$ is equivalent to a subsequence of $(e_{k})$. Sufficient conditions are given for a partly modified mixed Tsirelson space to be subsequentially minimal, and connections with Bourgain's ℓ¹-index are established. It is also shown that a large class of mixed Tsirelson spaces fails to be subsequentially minimal in a strong sense.

Kategorie tematyczne

• 46B20: Geometry and structure of normed linear spaces
• 46B45: Banach sequence spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2008
• Tom: 187
• Numer: 3
• Strony: 233-263

Daty

wydano

2008

Twórcy

autor

Denka Kutzarova

• Institute of Mathematics, Bulgarian Academy of Sciences
• Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL 61801, U.S.A.

autor

Denny H. Leung

• Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore 117543

autor

Antonis Manoussakis

• Department of Mathematics, University of Aegean, Karlovasi, Samos, GR 83200, Greece

autor

Wee-Kee Tang

• Mathematics and Mathematics Education, National Institute of Education, Nanyang Technological University, 1 Nanyang Walk, Singapore 637616

Identyfikatory

DOI

10.4064/sm187-3-3