Resumen de Topological characterization of weakly compact operators revisited

Antonio Miguel Peralta Pereira

• In this note we revise and survey some recent results established in [8]. We shall show that for each Banach space X, there exists a locally convex topology for X, termed the �Right Topology�, such that a linear map T, from X into a Banach space Y, is weakly compact, precisely when T is a continuous map from X, equipped with the �Right� topology, into Y equipped with the norm topology. We provide here a new and shorter proof of this result. We shall also survey the results concerning sequentially Right-to-norm continuous operators.