Lattice structures on some Banach spaces

Mastyło, Mieczysław

doi:10.1090/S0002-9939-2011-11151-1

Lattice structures on some Banach spaces
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by Mieczysław Mastyło

Proc. Amer. Math. Soc. 140 (2012), 1413-1422

DOI: https://doi.org/10.1090/S0002-9939-2011-11151-1

Published electronically: August 16, 2011

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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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