โ Scribed by Antonio Galbis; Alfredo Peris
No coin nor oath required. For personal study only.
In this note we treat some open problems of HEINRICH on ultrapowers of locally convex spaces. In section 1 we investigate the localization of bounded sets in the full ultrapower of a locally convex space, in particular the coincidence of the full and the bounded ultrapower, mainly concentrating in the case of (DF)-spaces. In section 2 we provide a partial answer to a question of HEINRICH on commutativity of strict inductive limits and ultrapowers. In section 3 we analyze the relation between some natural candidates for the notion of superreflexivity in the setting of Frichet spaces. We give an example of a Frkchet-Schwartz space which is not the projective limit of a sequence of superreflexive Banach spaces.
๐ SIMILAR VOLUMES
## Abstract We provided an answer to an open problem of A. Pietsch by giving a direct construction of the bornologically surjective hull ๐ฒ^bsur^ of an operator ideal ๐ฒ on __LCS's.__ Discussion of some extension problems of operator ideals were given.