Interpolation of compact operators by the methods of Calderón and Gustavsson-Peetre
Michael Cwikel, Nigel J. Kalton
Abstract
Let X=(X0,X1) and Y=(Y0,Y1) be Banach couples and suppose T: X Y is a linear operator such that T:X0 Y0 is compact. We consider the question whether the operator T:[X0,X1]θ [Y0,Y1]θ is compact and show a positive answer under a variety of conditions. For example it suffices that X0 be a UMD-space or that X0 is reflexive and there is a Banach space so that X0=[W,X1]α for some 0<α<1.
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