K-monotone weighted couples of banach lattices

K. E. Tikhomirov

doi:10.1134/S0037446606010162

K-monotone weighted couples of banach lattices

K. E. Tikhomirov

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We give a criterion for the uniform relative K-monotonicity of weighted couples (X,X(w₁)) and (X,X(w₂)), where X is some Banach lattice of measurable functions with the Fatou property while w₁ and w₂ are weight functions. Using the criterion, we prove some corollaries for sequence spaces and arbitrary Banach lattices.

Original language	English (US)
Pages (from-to)	147-158
Number of pages	12
Journal	Siberian Mathematical Journal
Volume	52
Issue number	1
DOIs	https://doi.org/10.1134/S0037446606010162
State	Published - Jan 2011

All Science Journal Classification (ASJC) codes

General Mathematics

Keywords

Calderón-Mityagin couple
K-monotone couple
interpolation of operators
weighted couple

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10.1134/S0037446606010162

Cite this

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abstract = "We give a criterion for the uniform relative K-monotonicity of weighted couples (X,X(w1)) and (X,X(w2)), where X is some Banach lattice of measurable functions with the Fatou property while w1 and w2 are weight functions. Using the criterion, we prove some corollaries for sequence spaces and arbitrary Banach lattices.",

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AB - We give a criterion for the uniform relative K-monotonicity of weighted couples (X,X(w1)) and (X,X(w2)), where X is some Banach lattice of measurable functions with the Fatou property while w1 and w2 are weight functions. Using the criterion, we prove some corollaries for sequence spaces and arbitrary Banach lattices.

KW - Calderón-Mityagin couple

KW - K-monotone couple

KW - interpolation of operators

KW - weighted couple

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DO - 10.1134/S0037446606010162

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EP - 158

JO - Siberian Mathematical Journal

JF - Siberian Mathematical Journal

IS - 1

ER -

K-monotone weighted couples of banach lattices

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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