The -indices of Tsirelson type spaces

Authors:
Denny H. Leung and Wee-Kee Tang

Journal:
Proc. Amer. Math. Soc. **131** (2003), 511-521

MSC (2000):
Primary 46B20; Secondary 05C05

DOI:
https://doi.org/10.1090/S0002-9939-02-06586-3

Published electronically:
June 3, 2002

MathSciNet review:
1933342

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Abstract | References | Similar Articles | Additional Information

Abstract: If and are countable ordinals such that , denote by the completion of with respect to the implicitly defined norm

where the supremum is taken over all finite subsets of such that and . It is shown that the Bourgain -index of is . In particular, if in Cantor normal form and is not a limit ordinal, then there exists a Banach space whose -index is .

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Additional Information

**Denny H. Leung**

Affiliation:
Department of Mathematics, National University of Singapore, Singapore 117543

Email:
matlhh@nus.edu.sg

**Wee-Kee Tang**

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

Email:
wktang@nie.edu.sg

DOI:
https://doi.org/10.1090/S0002-9939-02-06586-3

Received by editor(s):
March 7, 2001

Received by editor(s) in revised form:
July 10, 2001, and September 20, 2001

Published electronically:
June 3, 2002

Communicated by:
N. Tomczak-Jaegermann

Article copyright:
© Copyright 2002
American Mathematical Society