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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

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

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

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