Semilattice structures of spreading models

Authors:
Denny H. Leung and Wee-Kee Tang

Journal:
Proc. Amer. Math. Soc. **136** (2008), 3561-3570

MSC (2000):
Primary 46B20, 46B15

Published electronically:
May 22, 2008

MathSciNet review:
2415040

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Abstract | References | Similar Articles | Additional Information

Abstract: Given a Banach space , denote by the set of equivalence classes of spreading models of generated by normalized weakly null sequences in . It is known that is a semilattice, i.e., it is a partially ordered set in which every pair of elements has a least upper bound. We show that every countable semilattice that does not contain an infinite increasing sequence is order isomorphic to for some separable Banach space .

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Additional Information

**Denny H. Leung**

Affiliation:
Department of Mathematics, National University of Singapore, 2 Science Drive 2, 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:
weekee.tang@nie.edu.sg

DOI:
http://dx.doi.org/10.1090/S0002-9939-08-09494-X

Keywords:
Spreading models,
semilattices,
Lorentz sequence spaces

Received by editor(s):
August 1, 2007

Published electronically:
May 22, 2008

Additional Notes:
The research of the first author was partially supported by AcRF project no. R-146-000-086-112

Communicated by:
N. Tomczak-Jaegermann

Article copyright:
© Copyright 2008
American Mathematical Society