Interpolation of compact operators by general interpolation methods

摘要

Let a linear operator T act compactly from a Banach couple (X) over right arrow := (X-0, X-1) in a Banach lattice couple (B) over right arrow: = (B-0, B-1). If both B-i have absolutely continuous norm, then any interpolation functor F preserves two-sided compactness of T. The same holds if only one of B-i satisfies the above condition and F is a quasipower regular functor. The similar results are true for operators acting from (B) over right arrow in (X) over right arrow under the above formulated assumptions for simultaneously (B) over right arrow and its dual (B) over right arrow'. (C) 2014 Elsevier Inc. All rights reserved.