Bulletin of the Belgian Mathematical Society - Simon Stevin

A characterization of alternatively convex or smooth Banach spaces

H. Espid and R. Alizadeh

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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.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 25, Number 1 (2018), 121-127.

Dates
First available in Project Euclid: 11 April 2018

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1523412059

Mathematical Reviews number (MathSciNet)
MR3784510

Zentralblatt MATH identifier
06882546

Subjects
Primary: 46B20: Geometry and structure of normed linear spaces 47A12: Numerical range, numerical radius

Keywords
rotundity smoothness acs spaces numerical range

Citation

Espid, H.; Alizadeh, R. A characterization of alternatively convex or smooth Banach spaces. Bull. Belg. Math. Soc. Simon Stevin 25 (2018), no. 1, 121--127. https://projecteuclid.org/euclid.bbms/1523412059


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