The Bishop–Phelps–Bollobás property for operators from c0 into some Banach spaces

We exhibit a new class of Banach spaces Y   such that the pair (c0,Y)(c0,Y) has the Bishop–Phelps–Bollobás property for operators. This class contains uniformly convex Banach spaces and spaces with the property β of Lindenstrauss. We also provide new examples of spaces in this class.