Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Gowers' dichotomy for asymptotic structure


Author: R. Wagner
Journal: Proc. Amer. Math. Soc. 124 (1996), 3089-3095
MSC (1991): Primary 46B20
DOI: https://doi.org/10.1090/S0002-9939-96-03718-5
MathSciNet review: 1363438
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper Gowers' dichotomy is extended to the context of weaker forms of unconditionality, most notably asymptotic unconditionality. A general dichotomic principle is demonstrated; a Banach space has either a subspace with some unconditionality property, or a subspace with a corresponding `proximity of subspaces' property.


References [Enhancements On Off] (What's this?)

  • [AD] S. A. Argyros and I. Delyianni, Examples of asymptotically-$l_1$ Banach spaces, preprint.
  • [C] P. G. Casazza, Some questions arising from the homogeneous Banach space problem, in Banach Spaces, Contemp. Math. 144 (1993), 35--52. MR 93j:4601b
  • [G] W. T. Gowers, A new dichotomy of Banach-spaces, preprint.
  • [GM] W. T. Gowers and B. Maurey, The unconditional basic sequence problem, J. Amer.Math. Soc. 6 (1993), 851--874. MR 94k:46021
  • [H] P. Habala, A Banach space whose subspaces do not have the Gordon-Lewis property, preprint.
  • [MMiT] B. Maurey, V. D. Milman and N. Tomzcak-Jaegermann, Asymptotic infinite-dimensional theory of Banach-spaces, Geometric Aspects of Functional Analysis, Operator Theory Adv. Appl., vol. 77, Birkhäuser, Basel, 1995, pp. 149--175.
  • [MiSh] V. D. Milman and M. Sharir, Shrinking minimal systems and complementation of $l_p^n$-spaces in reflexive Banach spaces, Proc. London Math. Soc. 39 (1979), 1--29. MR 80j:46031
  • [O] E. Odell, Private communication.
  • [OS] E. Odell and T. Schumplrecht, A Banach space block finitely universal for monotone bases, preprint.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 46B20

Retrieve articles in all journals with MSC (1991): 46B20


Additional Information

R. Wagner
Affiliation: School of Mathematical Sciences, Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978, Israel
Email: pasolini@math.tau.ac.il

DOI: https://doi.org/10.1090/S0002-9939-96-03718-5
Received by editor(s): March 27, 1995
Additional Notes: The author was partially supported by BSF
Communicated by: Dale Alspach
Article copyright: © Copyright 1996 American Mathematical Society

American Mathematical Society