p-Envelopes of non-locally convex F-spaces
Tom 57 / 1992
Annales Polonici Mathematici 57 (1992), 121-134 DOI: 10.4064/ap-57-2-121-134
The p-envelope of an F-space is the p-convex analogue of the Fréchet envelope. We show that if an F-space is locally bounded (i.e., a quasi-Banach space) with separating dual, then the p-envelope coincides with the Banach envelope only if the space is already locally convex. By contrast, we give examples of F-spaces with are not locally bounded nor locally convex for which the p-envelope and the Fréchet envelope are the same.