Spreading sequences in JT

Helga Fetter; B. Gamboa de Buen

Studia Mathematica (1997)

  • Volume: 125, Issue: 1, page 57-66
  • ISSN: 0039-3223

Abstract

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We prove that a normalized non-weakly null basic sequence in the James tree space JT admits a subsequence which is equivalent to the summing basis for the James space J. Consequently, every normalized basic sequence admits a spreading subsequence which is either equivalent to the unit vector basis of l 2 or to the summing basis for J.

How to cite

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Fetter, Helga, and Gamboa de Buen, B.. "Spreading sequences in JT." Studia Mathematica 125.1 (1997): 57-66. <http://eudml.org/doc/216421>.

@article{Fetter1997,
abstract = {We prove that a normalized non-weakly null basic sequence in the James tree space JT admits a subsequence which is equivalent to the summing basis for the James space J. Consequently, every normalized basic sequence admits a spreading subsequence which is either equivalent to the unit vector basis of $l_2$ or to the summing basis for J.},
author = {Fetter, Helga, Gamboa de Buen, B.},
journal = {Studia Mathematica},
keywords = {normalized non-weakly null basic sequence; James tree space; summing basis; spreading subsequence},
language = {eng},
number = {1},
pages = {57-66},
title = {Spreading sequences in JT},
url = {http://eudml.org/doc/216421},
volume = {125},
year = {1997},
}

TY - JOUR
AU - Fetter, Helga
AU - Gamboa de Buen, B.
TI - Spreading sequences in JT
JO - Studia Mathematica
PY - 1997
VL - 125
IS - 1
SP - 57
EP - 66
AB - We prove that a normalized non-weakly null basic sequence in the James tree space JT admits a subsequence which is equivalent to the summing basis for the James space J. Consequently, every normalized basic sequence admits a spreading subsequence which is either equivalent to the unit vector basis of $l_2$ or to the summing basis for J.
LA - eng
KW - normalized non-weakly null basic sequence; James tree space; summing basis; spreading subsequence
UR - http://eudml.org/doc/216421
ER -

References

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  1. [1] I. Amemiya and T. Ito, Weakly null sequences in James spaces on trees, Kodai Math. J. 4 (1981), 418-425. Zbl0482.46008
  2. [2] A. Andrew, Spreading basic sequences and subspaces of James' quasireflexive space, Math. Scand. 48 (1981), 109-118. Zbl0439.46010
  3. [3] B. Beauzamy et J.-T. Lapresté, Modèles étalés des espaces de Banach, Travaux en Cours, Hermann, Paris 1984. Zbl0553.46012
  4. [4] G. Berg, On James spaces, Ph.D. thesis, The University of Texas, Austin, Texas, 1996. Zbl0852.46020
  5. [5] H. Fetter and B. Gamboa de Buen, The James Forest, London Math. Soc. Lecture Note Ser. 236, Cambridge Univ. Press, 1997. Zbl0878.46010
  6. [6] H. Fetter and B. Gamboa de Buen, The spreading models of the space = ( J ⨁ J ⨁ . . . ) l 2 , Bol. Soc. Mat. Mexicana 2 (3) (1996), 139-146. Zbl0867.46015
  7. [7] J. Hagler, A counterexample to several questions about Banach spaces, Studia Math. 60 (1977), 289-308. Zbl0387.46015
  8. [8] R. C. James, Bases and reflexivity of Banach spaces, Ann. of Math. 52 (1950), 518-527. Zbl0039.12202
  9. [9] R. C. James, A separable somewhat reflexive Banach space with nonseparable dual, Bull. Amer. Math. Soc. 80 (1974), 738-743. Zbl0286.46018

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