K-monotone weighted couples of Banach lattices (Q536640)

This is a paper, surely interesting for linear interpolation people. The main theorem, Theorem 1, gives an equivalence between the uniform relative K-monotonicity of Banach couples of weighted spaces and a special kind of decomposability of Banach lattices. The result is interesting because previous connected results [e.g., \textit{M. Cwikel}, \textit{P. G. Nilsson} and \textit{G. Schechtman}, ``Interpolation of weighted Banach lattices. A characterization of relatively decomposable Banach lattices'', Mem. Am. Math. Soc. 787 (2003; Zbl 1044.46018)] work generally only for weighted Lebesgue spaces.