Narrow Operators on Bochner L₁-Spaces - Boyko, K.; Kadets, V.; Werner, D. (Журнал математической физики, анализа, геометрии, 2006)
Narrow operators on L₁(μ;X)-spaces are studied. We present a sufficient criterion for such an operator to be narrow that resembles the characterization on narrow operators on L₁(μ) and show that the criterion is necessary for certain X, e.g., for spaces with the RNP.