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)



Weakly null sequences with an unconditional subsequence

Author: Alexander D. Arvanitakis
Journal: Proc. Amer. Math. Soc. 134 (2006), 67-74
MSC (2000): Primary 05D10, 46B15
Published electronically: August 12, 2005
MathSciNet review: 2170544
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In the present paper we provide sufficient conditions such that a normalized pointwise convergent to zero sequence in $C(K, X)$ with $K$ a compact space and $X$ a Banach space has an unconditional subsequence.

As a consequence we obtain that any such sequence of functions $(f_n)_n$ with finite and uniformly bounded cardinality of their range admits an unconditional subsequence.

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

  • 1. S. A. Argyros, G. Godefroy, and H. P. Rosenthal.
    Descriptive set theory and Banach spaces.
    In Handbook of the geometry of Banach spaces, Vol. 2, pages 1007-1069. North-Holland, Amsterdam, 2003. MR 1999190 (2004g:46002)
  • 2. S. A. Argyros, S. Mercourakis, and A. Tsarpalias.
    Convex unconditionality and summability of weakly null sequences.
    Israel J. Math., 107:157-193, 1998. MR 1658551 (99m:46021)
  • 3. E. Ellentuck.
    A new proof that analytic sets are Ramsey.
    J. Symbolic Logic, 39:163-165, 1974. MR 0349393 (50:1887)
  • 4. J. Elton.
    Weakly null normalized sequences in Banach spaces.
    Ph.D. thesis, 1978.
  • 5. F. Galvin and K. Prikry.
    Borel sets and Ramsey's theorem.
    J. Symbolic Logic, 38:193-198, 1973. MR 0337630 (49:2399)
  • 6. I. Gasparis, E Odell, and B. Wahl.
    Weakly null sequences in the Banach space $C(K).$
  • 7. J. Lopez-Abad and S. Todorcevic.
    Unconditional subsequences of weakly null sequences.
    In preparation, 2004.
  • 8. B. Maurey and H. P. Rosenthal.
    Normalized weakly null sequence with no unconditional subsequence.
    Studia Math., 61(1):77-98, 1977. MR 0438091 (55:11010)
  • 9. E. Odell.
    Applications of Ramsey theorems to Banach space theory.
    In Notes in Banach spaces, pages 379-404. Univ. Texas Press, Austin, Tex., 1980. MR 0606226 (83g:46018)
  • 10. J. Silver.
    Every analytic set is Ramsey.
    J. Symbolic Logic, 35:60-64, 1970. MR 0332480 (48:10807)
  • 11. S. Todorcevic.
    High-dimensional Ramsey theory.
    Preprint, CRM, 2004.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 05D10, 46B15

Retrieve articles in all journals with MSC (2000): 05D10, 46B15

Additional Information

Alexander D. Arvanitakis
Affiliation: Department of Mathematics, National Technical University of Athens, Zografou Campus, 15780, Athens, Greece

Received by editor(s): April 2, 2004
Received by editor(s) in revised form: September 1, 2004
Published electronically: August 12, 2005
Additional Notes: The author was partially supported by EPEAEK research program Pythagoras
Communicated by: N. Tomczak-Jaegermann
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society