p-Envelopes of non-locally convex F-spaces

C. M. Eoff

Annales Polonici Mathematici (1992)

  • Volume: 57, Issue: 2, page 121-134
  • ISSN: 0066-2216

Abstract

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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.

How to cite

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C. M. Eoff. "p-Envelopes of non-locally convex F-spaces." Annales Polonici Mathematici 57.2 (1992): 121-134. <http://eudml.org/doc/262488>.

@article{C1992,
abstract = {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.},
author = {C. M. Eoff},
journal = {Annales Polonici Mathematici},
keywords = {p-envelope; non-locally convex F-space; multiplier; -envelope of an -space; -convex analogue of the Fréchet envelope; locally bounded; quasi-Banach space; separating dual},
language = {eng},
number = {2},
pages = {121-134},
title = {p-Envelopes of non-locally convex F-spaces},
url = {http://eudml.org/doc/262488},
volume = {57},
year = {1992},
}

TY - JOUR
AU - C. M. Eoff
TI - p-Envelopes of non-locally convex F-spaces
JO - Annales Polonici Mathematici
PY - 1992
VL - 57
IS - 2
SP - 121
EP - 134
AB - 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.
LA - eng
KW - p-envelope; non-locally convex F-space; multiplier; -envelope of an -space; -convex analogue of the Fréchet envelope; locally bounded; quasi-Banach space; separating dual
UR - http://eudml.org/doc/262488
ER -

References

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  3. [3] P. L. Duren, Theory of H p Spaces, Academic Press, New York 1970. Zbl0215.20203
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  13. [13] J. H. Shapiro, Mackey topologies, reproducing kernels, and diagonal maps on the Hardy and Bergman spaces, Duke Math. J. 43 (1976), 187-202. Zbl0354.46036
  14. [14] J. H. Shapiro, Remarks on F-spaces of analytic functions, in: Banach Spaces of Analytic Functions, Lecture Notes in Math. 604, Springer, Berlin 1977, 107-124. 
  15. [15] M. Stoll, Mean growth and Taylor coefficients of some topological algebras of analytic functions, Ann. Polon. Math. 35 (1977), 139-158. Zbl0377.30036
  16. [16] N. Yanagihara, Multipliers and linear functionals for the class N⁺, Trans. Amer. Math. Soc. 180 (1973), 449-461. Zbl0243.46036
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  18. [18] A. I. Zayed, Topological vector spaces of analytic functions, Complex Variables 2 (1983), 27-50. Zbl0495.46019

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