Semilattice structures of spreading models
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- by Denny H. Leung and Wee-Kee Tang PDF
- Proc. Amer. Math. Soc. 136 (2008), 3561-3570 Request permission
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 $X$.References
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Additional Information
- Denny H. Leung
- Affiliation: Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore 117543
- MR Author ID: 113100
- 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
- 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
- © Copyright 2008 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 136 (2008), 3561-3570
- MSC (2000): Primary 46B20, 46B15
- DOI: https://doi.org/10.1090/S0002-9939-08-09494-X
- MathSciNet review: 2415040