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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: 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

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.

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