Real Interpolation of Compact Operators between Quasi-Banach Spaces

Abstract

Let (A(0)A(1)) and (B-0,B-1) be couples of quasi-Banach spaces and let T be a linear operator. We prove that if T:A(0) --> B-0 is compact and T: A(1) --> B-1 is bounded, then T: (A(0),A(1))(theta,q) --> (B-0,B-1)(theta,q) is also compact. Some results on the structure of minimal and maximal interpolation methods are also established.