Resumen de Hahn-Banach theorem for the compact convergence topology and applications to approximation properties

Changsun Choi, Ju Myung Kim

• Let X and Y be Banach spaces. We show that if X* or Y* has the Radon-Nikodym property and S is a space of weak* to weak continuous compact operators from X* into Y, then given e>0 every norm continuous linear functional f on S can be extended to a linear functional ? on B(X*,Y), without increasing the norm more than e so that ? is continuous with respect to the compact convergence topology. From this result we obtain various applications