On the Bishop-Phelps-Bollobas property for numerical radius in   C(K)-spaces
  We study the Bishop-Phelps-Bollobas property for numerical radius within the framework of C(K) spaces. We present several sufficient conditions on a compact space K ensuring that C(K) has the Bishop-Phelps-Bollobas property for numerical radius. In particular, we show that C(K) has such property whenever K is metrizable. 
Antonio Avil\'es, Antonio J. Guirao, Jos\'e Rodr\'iguez
math.FA