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A note on bump functions that locally depend on finitely many coordinates

Published online by Cambridge University Press:  17 April 2009

M. Fabian  and
V. Zizler
M. Fabian
Affiliation:
Mathematical InstituteCzech Academy of SciencesŽitná 25, 11567 Prague 1Czech Republic, e-mail: fabian@karlin.mff.cuni.cz
V. Zizler
Affiliation:
Department of Mathematical AnalysisFaculty of Mathematics and PhysicsCharles UniversitySokolovská 83, 18600 Prague 8Czech Republic and Department of Mathematics, University of Alberta, Edmonton, T6G 2G1 Alberta, Canada, e-mail: vzizler@vega.math.ualberta.ca
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Abstract

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We show that if a continuous bump function on a Banach space X locally depends on finitely many elements of a set F in X*, then the norm closed linear span of F equals to X*. Some corollaries for Markuševič bases and Asplund spaces are derived.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 56 , Issue 3 , December 1997 , pp. 447 - 451
Copyright
Copyright © Australian Mathematical Society 1997

References

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