Spreading sequences in JT

• Autorzy: Helga Fetter , B. Gamboa de Buen
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 46B20: Geometry and structure of normed linear spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1997
• Tom: 125
• Numer: 1
• Strony: 57-66

Daty

wydano

1997

otrzymano

1996-07-04

poprawiono

1997-02-19

Twórcy

autor

Helga Fetter

• Centro de Investigación en Matemáticas, Apartado Postal 402, 36000 Guanajuato, Guanajuato, México

autor

B. Gamboa de Buen

• Centro de Investigación en Matemáticas, Apartado Postal 402, 36000 Guanajuato, Guanajuato, México

Bibliografia

• [1] I. Amemiya and T. Ito, Weakly null sequences in James spaces on trees, Kodai Math. J. 4 (1981), 418-425.
• [2] A. Andrew, Spreading basic sequences and subspaces of James' quasireflexive space, Math. Scand. 48 (1981), 109-118.
• [3] B. Beauzamy et J.-T. Lapresté, Modèles étalés des espaces de Banach, Travaux en Cours, Hermann, Paris 1984.
• [4] G. Berg, On James spaces, Ph.D. thesis, The University of Texas, Austin, Texas, 1996.
• [5] H. Fetter and B. Gamboa de Buen, The James Forest, London Math. Soc. Lecture Note Ser. 236, Cambridge Univ. Press, 1997.
• [6] H. Fetter and B. Gamboa de Buen, The spreading models of the space $𝕁=(J⨁ J⨁...)_{l_2}$, Bol. Soc. Mat. Mexicana 2 (3) (1996), 139-146.
• [7] J. Hagler, A counterexample to several questions about Banach spaces, Studia Math. 60 (1977), 289-308.
• [8] R. C. James, Bases and reflexivity of Banach spaces, Ann. of Math. 52 (1950), 518-527.
• [9] R. C. James, A separable somewhat reflexive Banach space with nonseparable dual, Bull. Amer. Math. Soc. 80 (1974), 738-743.