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.
All Science Journal Classification (ASJC) codes
- Calderón-Mityagin couple
- K-monotone couple
- interpolation of operators
- weighted couple