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K-monotone weighted couples of banach lattices

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Abstract

We give a criterion for the uniform relative K-monotonicity of weighted couples (X,X(w 1)) and (X,X(w 2)), where X is some Banach lattice of measurable functions with the Fatou property while w 1 and w 2 are weight functions. Using the criterion, we prove some corollaries for sequence spaces and arbitrary Banach lattices.

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Authors and Affiliations

  1. Samara State University, Samara, Russia

    K. E. Tikhomirov

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  1. K. E. Tikhomirov
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Correspondence to K. E. Tikhomirov.

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Original Russian Text Copyright © 2011 Tikhomirov K. E.

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Samara. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 52, No. 1, pp. 187–200, January–February, 2011.

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Tikhomirov, K.E. K-monotone weighted couples of banach lattices. Sib Math J 52, 147–158 (2011). https://doi.org/10.1134/S0037446606010162

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  • DOI: https://doi.org/10.1134/S0037446606010162

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