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Estimates for the Jung constant in Banach lattices

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Abstract

Sharp lower estimates for the Jung constantJ(E) in Banach latticesE satisfying an upperp-estimate and a lowerq-estimate are given. Moreover, the minimal value ofJ(E) with respect to equivalent renormings ofE is calculated inE=L p,q for finitep andq, as well as in more general spacesE. Finally, a nontrivial estimate for the radiusr L p,∞ (A) is obtained forA being a bounded sequence of disjointly supported functions inL p,∞ .

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Authors and Affiliations

  1. Mathematisches Institut, Universität Würzburg, Am Hubland, D-97074, Würzburg, Germany

    Jürgen Appell

  2. Dipartimento di Matematica Applicata, Università di Firenze, Via S. Marta 3, I-50139, Firenze, Italy

    Carlo Franchetti

  3. Matematicheskij Fakul’tet, Voronezhskij Gosuniversitet, Universitetskaya pl. 1, R-394693, Voronezh, Russian Federation

    Evgenij M. Semenov

Authors
  1. Jürgen Appell
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  2. Carlo Franchetti
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  3. Evgenij M. Semenov
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Correspondence to Jürgen Appell.

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Appell, J., Franchetti, C. & Semenov, E.M. Estimates for the Jung constant in Banach lattices. Isr. J. Math. 116, 171–187 (2000). https://doi.org/10.1007/BF02773217

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  • DOI: https://doi.org/10.1007/BF02773217

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