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1992 | 57 | 2 | 121-134
Tytuł artykułu

p-Envelopes of non-locally convex F-spaces

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EN
Abstrakty
EN
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.
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autor
  • Department of Mathematical Sciences, University of Arkansas, Fayetteville, Arkansas 72701, U.S.A.
Bibliografia
  • [1] A. B. Aleksandrov, Essays on non-locally convex Hardy classes, in: Complex Analysis and Spectral Theory, Lecture Notes in Math. 864, Springer, Berlin 1981, 1-89.
  • [2] R. R. Coifman and R. Rochberg, Representation theorems for holomorphic and harmonic functions in $L^p$, Astérisque 77 (1980), 11-66.
  • [3] P. L. Duren, Theory of $H^p$ Spaces, Academic Press, New York 1970.
  • [4] P. L. Duren, B. W. Romberg and A. L. Shields, Linear functionals on $H^p$ spaces with 0 < p < 1, J. Reine Angew. Math. 238 (1969), 32-60.
  • [5] C. M. Eoff, Fréchet envelopes of certain algebras of analytic functions, Michigan Math. J. 35 (1988), 413-426.
  • [6] N. J. Kalton, Analytic functions in non-locally convex spaces and applications, Studia Math. 83 (1986), 275-303.
  • [7] N. J. Kalton, N. T. Peck and J. W. Roberts, An F-space Sampler, London Math. Soc. Lecture Note Ser. 89, Cambridge Univ. Press, 1984.
  • [8] J. E. McCarthy, Topologies on the Smirnov class, to appear.
  • [9] N. Mochizuki, Algebras of holomorphic functions between $H^p$ and $N_*$, Proc. Amer. Math. Soc. 105 (1989), 898-902.
  • [10] M. Nawrocki, Linear functionals on the Smirnov class of the unit ball in $ℂ^n$, Ann. Acad. Sci. Fenn. AI 14 (1989), 369-379.
  • [11] M. Nawrocki, The Fréchet envelopes of vector-valued Smirnov classes, Studia Math. 94 (1989), 163-177.
  • [12] J. W. Roberts and M. Stoll, Prime and principal ideals in the algebra N⁺, Arch. Math. (Basel) 27 (1976), 387-393; Correction, ibid. 30 (1978), 672.
  • [13] J. H. Shapiro, Mackey topologies, reproducing kernels, and diagonal maps on the Hardy and Bergman spaces, Duke Math. J. 43 (1976), 187-202.
  • [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] M. Stoll, Mean growth and Taylor coefficients of some topological algebras of analytic functions, Ann. Polon. Math. 35 (1977), 139-158.
  • [16] N. Yanagihara, Multipliers and linear functionals for the class N⁺, Trans. Amer. Math. Soc. 180 (1973), 449-461.
  • [17] N. Yanagihara, The containing Fréchet space for the class N⁺, Duke Math. J. 40 (1973), 93-103.
  • [18] A. I. Zayed, Topological vector spaces of analytic functions, Complex Variables 2 (1983), 27-50.
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Bibliografia
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bwmeta1.element.bwnjournal-article-apmv57z2p121bwm
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