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Lattice structures on some Banach spaces

Author: Mieczysław Mastyło
Journal: Proc. Amer. Math. Soc. 140 (2012), 1413-1422
MSC (2010): Primary 46E30, 46B03, 46M35
Published electronically: August 16, 2011
MathSciNet review: 2869126
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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

Keywords: Banach lattices, lattice structures, positive operators, positive interpolation functor, Lorentz spaces, Marcinkiewicz spaces, Calderón-Lozanovskii spaces
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
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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