The Bishop-Phelps-Bollobas Property on the Space of c(0)-Sum

The main purpose of this paper is to study Bishop-Phelps-Bollobas type properties on c(0) sum of Banach spaces. Among other results, we show that the pair (c(0)(X), Y) has the Bishop-Phelps-Bollob ' as property (in short, BPBp) for operators whenever X is uniformly convex and Y is (complex) uniformly convex. We also prove that the pair (c(0)(X), c(0)(X)) has the BPBp for bilinear forms whenever X is both uniformly convex and uniformly smooth. These extend the previously known results that (c(0), Y) has the BPBp for operators whenever Y is uniformly convex and (c(0), c(0)) has the BPBp for bilinear forms. We also obtain some results on a local BPBp which is called L-p,L- p for both operators and bilinear forms.