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march 2018 A characterization of alternatively convex or smooth Banach spaces
H. Espid, R. Alizadeh
Bull. Belg. Math. Soc. Simon Stevin 25(1): 121-127 (march 2018). DOI: 10.36045/bbms/1523412059

Abstract

In this paper, we give a characterization of alternatively convex or smooth Banach spaces. In fact we prove that every normaloid numerical radius attaining operator on a Banach space $X$ is radialoid if and only if $X$ is alternatively convex or smooth. In addition, we show that every compact normaloid operator on $X$ is radialoid if and only if every rank one normaloid operator on X is radialoid. Finally we present some types of Banach spaces on which the compact normaloid operators are radialoid.

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H. Espid. R. Alizadeh. "A characterization of alternatively convex or smooth Banach spaces." Bull. Belg. Math. Soc. Simon Stevin 25 (1) 121 - 127, march 2018. https://doi.org/10.36045/bbms/1523412059

Information

Published: march 2018
First available in Project Euclid: 11 April 2018

zbMATH: 06882546
MathSciNet: MR3784510
Digital Object Identifier: 10.36045/bbms/1523412059

Subjects:
Primary: 46B20, 47A12

Rights: Copyright © 2018 The Belgian Mathematical Society

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Vol.25 • No. 1 • march 2018
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