Spreading sequences in JT
Fetter, Helga ; Gamboa de Buen, B.
Studia Mathematica, Tome 122 (1997), p. 57-66 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

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 l2 or to the summing basis for J.

Publié le : 1997-01-01
EUDML-ID : urn:eudml:doc:216421 
@article{bwmeta1.element.bwnjournal-article-smv125i1p57bwm,
     author = {Helga Fetter and B. Gamboa de Buen},
     title = {Spreading sequences in JT},
     journal = {Studia Mathematica},
     volume = {122},
     year = {1997},
     pages = {57-66},
     zbl = {0898.46014},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv125i1p57bwm}
}

Fetter, Helga; Gamboa de Buen, B. Spreading sequences in JT. Studia Mathematica, Tome 122 (1997) pp. 57-66. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv125i1p57bwm/

[00000] [1] I. Amemiya and T. Ito, Weakly null sequences in James spaces on trees, Kodai Math. J. 4 (1981), 418-425. | Zbl 0482.46008

[00001] [2] A. Andrew, Spreading basic sequences and subspaces of James' quasireflexive space, Math. Scand. 48 (1981), 109-118. | Zbl 0439.46010

[00002] [3] B. Beauzamy et J.-T. Lapresté, Modèles étalés des espaces de Banach, Travaux en Cours, Hermann, Paris 1984. | Zbl 0553.46012

[00003] [4] G. Berg, On James spaces, Ph.D. thesis, The University of Texas, Austin, Texas, 1996. | Zbl 0852.46020

[00004] [5] H. Fetter and B. Gamboa de Buen, The James Forest, London Math. Soc. Lecture Note Ser. 236, Cambridge Univ. Press, 1997. | Zbl 0878.46010

[00005] [6] H. Fetter and B. Gamboa de Buen, The spreading models of the space =(J⨁J⨁...)l2, Bol. Soc. Mat. Mexicana 2 (3) (1996), 139-146. | Zbl 0867.46015

[00006] [7] J. Hagler, A counterexample to several questions about Banach spaces, Studia Math. 60 (1977), 289-308. | Zbl 0387.46015

[00007] [8] R. C. James, Bases and reflexivity of Banach spaces, Ann. of Math. 52 (1950), 518-527. | Zbl 0039.12202

[00008] [9] R. C. James, A separable somewhat reflexive Banach space with nonseparable dual, Bull. Amer. Math. Soc. 80 (1974), 738-743. | Zbl 0286.46018