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The Γ-opial property

Published online by Cambridge University Press:  17 April 2009

Monika Budzyńska ,
Tadeusz Kuczumow  and
Małgorzata Michalska
Monika Budzyńska
Affiliation:
Instytut Matematyki, UMCS, 20-031 Lublin, Poland, e-mail: monikab@golem.umcs.lublin.pl, tadek@golem.umcs.lublin.pl, daisy@golem.umcs.lublin.pl
Tadeusz Kuczumow
Affiliation:
Instytut Matematyki, UMCS, 20-031 Lublin, Poland, e-mail: monikab@golem.umcs.lublin.pl, tadek@golem.umcs.lublin.pl, daisy@golem.umcs.lublin.pl
Małgorzata Michalska
Affiliation:
Instytut Matematyki, UMCS, 20-031 Lublin, Poland, e-mail: monikab@golem.umcs.lublin.pl, tadek@golem.umcs.lublin.pl, daisy@golem.umcs.lublin.pl
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In this short paper we show that if (X, ∥ · ∥) is a Banach space, Γ a norming set for X and C is a nonempty, bounded and Γ sequentially compact subset of X, then in C the Γ-Opial condition for nets is equivalent to the Γ-Opial condition.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 73 , Issue 3 , June 2006 , pp. 473 - 476
Copyright
Copyright © Australian Mathematical Society 2006

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