IMPORTANT NOTICE

The AMS website will be down for maintenance on May 23 between 6:00am - 8:00am EDT. For questions please contact AMS Customer Service at cust-serv@ams.org or (800) 321-4267 (U.S. & Canada), (401) 455-4000 (Worldwide).

 

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)

 
 

 

Subsymmetric sequences and minimal spaces


Author: Anna Maria Pelczar
Journal: Proc. Amer. Math. Soc. 131 (2003), 765-771
MSC (2000): Primary 46B20; Secondary 46B15
DOI: https://doi.org/10.1090/S0002-9939-02-06594-2
Published electronically: July 2, 2002
MathSciNet review: 1937415
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We show that every Banach space saturated with subsymmetric basic sequences contains a minimal subspace.


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

  • [CJT] P. G. Casazza, W. B. Johnson and L. Tzafriri, On Tsirelson's space, Israel J. Math. 47 (1974), 191-21. MR 85m:46013
  • [CO] P. G. Casazza and E. Odell, Tsirelson's space and minimal subspaces, Texas Functional Analysis Seminar 1982/3, Longhorn Notes, University of Texas, pp. 61-72.
  • [G1] W. T. Gowers, A new dichotomy for Banach spaces, Geom. Funct. Anal. 6 (1996), 1083-1093. MR 97m:46017
  • [G2] W. T. Gowers, Infinite Ramsey theorem and some Banach-space dichotomies, preprint.
  • [GM] W. T. Gowers and B. Maurey, The unconditional basic sequence problem, J. Amer. Math. Soc. 6 (1993), 851-874. MR 94k:46021
  • [KM] K. Kuratowski and A. Mostowski, Teoria mnogosci, Monografie Matematyczne 27, Warszawa, 1978.
  • [LT] J. Lindenstrauss and L. Tzafriri, Classical Banach spaces, vol. I, Springer-Verlag, Berlin-New York, 1977. MR 58:17766
  • [M] B. Maurey, A note on Gowers' dichotomy theorem, Convex Geometric Analysis, vol. 34, Cambridge Univ. Press, Cambridge, 1999, pp. 149-157. MR 2000b:46015
  • [P] A. M. Pelczar, On Gowers' dichotomy, to be published in Recent Progress in Functional Analysis (K.D. Bierstedt, J. Bonet, M. Maestre, J. Schmets, eds.) Proceedings of Functional Analysis Valencia 2000, North-Holland Math. Studies.
  • [R] H. Rosenthal, A characterization of Banach spaces containing $\ell _{1}$, Proc. Nat. Acad. Sci. USA 71 (1974), 2411-2413. MR 50:10773
  • [S] Th. Schlumprecht, A complementably minimal Banach space not containing $c_{0}$ or $\ell _{p}$, Seminar Notes in Functional Analysis and PDE's, LSU, 1991-92, pp. 169-181.
  • [T1] E. Tutaj, O pewnych warunkach wystarczajacych do istnienia w przestrzeni Banacha ciagu bazowego bezwarunkowego (On some conditions sufficient for the existence of an unconditional basic sequence in a Banach space), Ph.D. Thesis, Uniwersytet Jagiellonski, Kraków, 1974.
  • [T2] E. Tutaj, On Schauder bases which are unconditional like, Bull. Polish Acad. Sci. Math. 33 (1985), 137-146. MR 87b:46010
  • [Z] P. Zbierski, lecture, Uniwersytet Warszawski, 1999.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 46B20, 46B15

Retrieve articles in all journals with MSC (2000): 46B20, 46B15


Additional Information

Anna Maria Pelczar
Affiliation: Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland
Email: apelczar@im.uj.edu.pl

DOI: https://doi.org/10.1090/S0002-9939-02-06594-2
Received by editor(s): July 10, 2001
Received by editor(s) in revised form: October 9, 2001
Published electronically: July 2, 2002
Communicated by: N. Tomczak-Jaegermann
Article copyright: © Copyright 2002 American Mathematical Society

American Mathematical Society