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On Banach spaces with few spreading models

Author(s): Bünyamin Sari
Journal: Proc. Amer. Math. Soc. 134 (2006), 1339-1345.
MSC (2000): Primary 46B20; Secondary 46B15
Posted: August 29, 2005
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Abstract: If the set of spreading models of a Banach space $X$is countable (up to equivalence), then it cannot contain a strictly increasing infinite chain of spreading models generated by normalized weakly null sequences. Moreover, such a space $X$ must have a spreading model which is `close' to $c_0$ or $\ell_p$ for some $1\le p<\infty$.

References:

[AOST]
G. Androulakis, E. Odell, Th. Schlumprecht and N. Tomczak-Jaegermann, On the structure of the spreading models of a Banach space, to appear in Canadian Journal of Math.

[BL]
B. Beauzamy and J.-T. Lapreste, Modèles étalés des espaces de Banach, Travaux en Cours, Hermann, Paris, 1984. MR 0770062 (86h:46024)

[FPR]
V. Ferenczi, A.M. Pelczar and C. Rosendal, On a question of Haskell P. Rosenthal concerning a characterization of $c\sb 0$ and $\ell\sb p$, Bull. London Math. Soc. 36 (2004), no. 3, 396-406. MR 2038727 (2004m:46026)

[OS]
E. Odell and T. Schlumprecht, On the richness of the set of $p$'s in Krivine's theorem, Geometric aspects of functional analysis (Israel, 1992-1994), 177-198, Oper. Theory Adv. Appl., 77, Birkhaüser, Basel, 1995.MR 1353459 (96i:46015)

[Sa]
B. Sari, Envelope functions and asymptotic structures in Banach spaces, Studia Math. 164 (2004), no. 3, 283-306.MR 2079954

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Additional Information:

Bünyamin Sari
Affiliation: Department of Mathematics, University of South Carolina, Columbia, South Carolina 29208
Email: bsari@math.sc.edu

DOI: 10.1090/S0002-9939-05-08078-0
PII: S 0002-9939(05)08078-0
Received by editor(s): November 2, 2004
Received by editor(s) in revised form: November 23, 2004
Posted: August 29, 2005
Communicated by: N. Tomczak-Jaegermann
Copyright of article: Copyright 2005, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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