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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Lattice structures on some Banach spaces
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by Mieczysław Mastyło PDF
Proc. Amer. Math. Soc. 140 (2012), 1413-1422 Request permission

Abstract:

The purpose of this paper is to study Banach lattice constants $d_n$ and $e_n$ originally introduced by Kalton. We prove an interpolation theorem for positive operators and derive estimates of the lattice constants for Banach lattices generated by positive interpolation functors. In particular, we provide estimates of these constants for Calderón-Loznanovskii spaces. We also find the lattice constants for Marcinkiewicz and Lorentz spaces. As applications, we prove results concerning lattice structures of studied spaces.
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Additional Information
  • Mieczysław Mastyło
  • Affiliation: Faculty of Mathematics and Computer Science, Adam Mickiewicz University and Institute of Mathematics, Polish Academy of Science (Poznań branch), Umultowska 87, 61-614 Poznań, Poland
  • MR Author ID: 121145
  • Email: mastylo@amu.edu.pl
  • Received by editor(s): August 15, 2010
  • Received by editor(s) in revised form: January 7, 2011
  • Published electronically: August 16, 2011
  • Additional Notes: This work was supported by the Committee of Scientific Research, Poland, grant No. 201 385034.

  • Dedicated: To the memory of Nigel Kalton
  • Communicated by: Marius Junge
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 140 (2012), 1413-1422
  • MSC (2010): Primary 46E30, 46B03, 46M35
  • DOI: https://doi.org/10.1090/S0002-9939-2011-11151-1
  • MathSciNet review: 2869126