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Proceedings of the American Mathematical Society
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
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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.


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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: http://dx.doi.org/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
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.