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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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: Given a Banach space $ X$, denote by $ SP_{w}(X)$ the set of equivalence classes of spreading models of $ X$ generated by normalized weakly null sequences in $ X$. It is known that $ SP_{w}(X)$ 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 $ SP_{w}(X)$ for some separable Banach space $ X$.


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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
PII: S 0002-9939(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