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1992 | 57 | 2 | 121-134
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p-Envelopes of non-locally convex F-spaces

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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.
Słowa kluczowe
  • Department of Mathematical Sciences, University of Arkansas, Fayetteville, Arkansas 72701, U.S.A.
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