Remotal sets in tensor product spaces and \(\varepsilon \)-remotality

Volume 19, Issue 2, pp 116--119 http://dx.doi.org/10.22436/jmcs.019.02.05

Publication Date: May 03, 2019 Submission Date: March 09, 2019 Revision Date: March 28, 2019 Accteptance Date: April 03, 2019

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Authors

H. Salameh - Department of Mathematics, University of Jordan, Amman, Jordan. R. Khalil - Department of Mathematics, University of Jordan, Amman, Jordan.

Abstract

Let \(X\) be a Banach space and \(E\) a bounded set in \(X\). For \(x\in X\), we set \(D(x,E)=\sup \{\Vert x-e\Vert :e\in E\}\). The set \(E\) is called remotal if for any \(x\in X\) there exists \(e\in E\) such that \(D(x,E)=\Vert x-e\Vert \). In this paper we prove some results on remotality in tensor product spaces. Further, we prove a main result "Every bounded set is \(% \varepsilon \)-remotal", where the concept of \( \epsilon \)-remotality was introduced introduced in last couple of years and studied by many authors.

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Keywords

• Remotal sets
• tensor product
• Banach spaces
• \(\epsilon \)-remotality

MSC

•  41A28
•  41A65

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