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Sibirskii Matematicheskii Zhurnal, 2011, Volume 52, Number 1, Pages 187–200 (Mi smj2188)  
K-monotone weighted couples of Banach lattices

K. E. Tikhomirov

Samara State University, Samara
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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.
Keywords: K-monotone couple, Calderón–Mityagin couple, weighted couple, interpolation of operators.
Received: 17.12.2009
English version:
Siberian Mathematical Journal, 2011, Volume 52, Issue 1, Pages 147–158
DOI: https://doi.org/10.1134/S0037446606010162
Bibliographic databases:
Document Type: Article
UDC: 517.982.27
Language: Russian
Citation: K. E. Tikhomirov, “K-monotone weighted couples of Banach lattices”, Sibirsk. Mat. Zh., 52:1 (2011), 187–200; Siberian Math. J., 52:1 (2011), 147–158
Citation in format AMSBIB
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    		Сибирский математический журнал Siberian Mathematical Journal
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