Sequential w-right continuity and summing operators

We continue the study of the w-right and strong* topologies in general Banach spaces started in 36, 37 and 35. We show that in L1(μ)-spaces the w-right convergence of sequences admits a simpler control. Some considerations about these topologies will be contemplated in the particular cases of C*-algebras and JB*-triples in connection with summing operators. We also study (sequential) w-right-norm and strong*-norm continuity for holomorphic mappings. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim