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 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.

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Weakly null sequences in the Banach space

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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

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.