|
Gowers' dichotomy for asymptotic structure
Author(s):
R.
Wagner
Journal:
Proc. Amer. Math. Soc.
124
(1996),
3089-3095.
MSC (1991):
Primary 46B20
Retrieve article in:
PDF
This article is available free of charge
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:
- [AD]
- S. A. Argyros and I. Delyianni, Examples of asymptotically-
 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
 -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:
10.1090/S0002-9939-96-03718-5
PII:
S 0002-9939(96)03718-5
Received by editor(s):
March 27, 1995
Additional Notes:
The author was partially supported by BSF
Communicated by:
Dale Alspach
Copyright of article:
Copyright
1996,
American Mathematical Society
|
Comments: webmaster@ams.org