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Weakly null sequences with an unconditional subsequence
Author(s):
Alexander
D.
Arvanitakis
Journal:
Proc. Amer. Math. Soc.
134
(2006),
67-74.
MSC (2000):
Primary 05D10, 46B15
Posted:
August 12, 2005
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Abstract:
In the present paper we provide sufficient conditions such that a normalized pointwise convergent to zero sequence in  with  a compact space and  a Banach space has an unconditional subsequence. As a consequence we obtain that any such sequence of functions  with finite and uniformly bounded cardinality of their range admits an unconditional subsequence.
References:
-
- 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 
Preprint. - 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.
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Additional Information:
Alexander
D.
Arvanitakis
Affiliation:
Department of Mathematics, National Technical University of Athens, Zografou Campus, 15780, Athens, Greece
Email:
aarva@math.ntua.gr
DOI:
10.1090/S0002-9939-05-07948-7
PII:
S 0002-9939(05)07948-7
Received by editor(s):
April 2, 2004
Received by editor(s) in revised form:
September 1, 2004
Posted:
August 12, 2005
Additional Notes:
The author was partially supported by EPEAEK research program Pythagoras
Communicated by:
N. Tomczak-Jaegermann
Copyright of article:
Copyright
2005,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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