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ON A FUNCTION MODULE WITH APPROXIMATE HYPERPLANE SERIES PROPERTY

Part of: Basic linear algebra Linear function spaces and their duals

Published online by Cambridge University Press:  03 July 2019

T. GRANDO Open the ORCID record for T. GRANDO [Opens in a new window]  and
M. L. LOURENÇO
T. GRANDO*
Affiliation:
Department of Mathematics, University of São Paulo, P.O. Box 66281, 05315-970, São Paulo, Brazil email tgrando@ime.usp.br
M. L. LOURENÇO
Affiliation:
Department of Mathematics, University of São Paulo, P.O. Box 66281, 05315-970, São Paulo, Brazil email mllouren@ime.usp.br
*
✉tgrando@ime.usp.br
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Abstract

We present a sufficient and necessary condition for a function module space $X$ to have the approximate hyperplane series property (AHSP). As a consequence, we have that the space ${\mathcal{C}}_{0}(L,E)$ of bounded and continuous $E$-valued mappings defined on the locally compact Hausdorff space $L$ has AHSP if and only if $E$ has AHSP.

Keywords

Bishop–Phelps–Bollobás property for operatorsapproximate hyperplane series propertyfunction module space

MSC classification

Primary: 46E25: Rings and algebras of continuous, differentiable or analytic functions
Secondary: 15A03: Vector spaces, linear dependence, rank
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 108 , Issue 3 , June 2020 , pp. 341 - 348
Copyright
© 2019 Australian Mathematical Publishing Association Inc.

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