Total convexity for powers of the norm in uniformly convex Banach spaces.
Butnariu, Dan, Iusem, Alfredo N., Resmerita, Elena (2000)
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Butnariu, Dan, Iusem, Alfredo N., Resmerita, Elena (2000)
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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.