The Bishop-Phelps-Bollobás property for operators defined on $c_0$-sum of Euclidean spaces

The main purpose of this paper is to study the Bishop-Phelps-Bollobás property for operators on $c_0$-sum of euclidean spaces. We show that the pair $(c_0\left({⨁}_{k=1}^{\mathrm{\infty }}{\mathrm{\ell }}_2^k\right),Y)$ has the Bishop-Phelps-Bollobás property for operators (shortly BPBp for operators) whenever $Y$ is a uniformly convex Banach space.