Uniformly \(\mu \)-continuous topologies on Köthe-Bochner spaces and Orlicz-Bochner spaces (Q2713583)

The author gives an account of locally solid topologies and studies mutual relations of uniformly \(\mu \)-continuous topologies, uniformly \(\mu \)-continuous solid pseudonorms, and uniformly summable pseudonorms. In Köthe-Bochner spaces he proves a characterization of uniformly \(\mu \)-continuous locally solid topologies in terms of uniformly summable pseudonorms. NEWLINENEWLINENEWLINEFurther, he shows that the finest uniformly \(\mu \)-continuous topology on an Orlicz-Bochner space is the generalized mixed topology, which coincides here with the concept of a strictly inductive limit of balanced topological spaces. In this frame a characterization of \(\gamma _{\varphi }\)-linear mappings is given.