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.
Citation
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