The Bishop-Phelps-Bollob\'as property for operators defined on $c_0$-sum of Euclidean spaces

Abstract

The main purpose of this paper is to study the Bishop-Phelps-Bollob\'as property for operators on $c_0$-sum of euclidean spaces. We show that the pair $ (c_0\left(\bigoplus^{\infty}_{k=1}\ell^{k}_{2} \right),Y)$ has the Bishop-Phelps-Bollob\'as property for operators (shortly BPBp for operators) whenever $Y$ is a uniformly convex Banach space.