Real Interpolation and Compact Linear-Operators

Abstract

We prove that if T: A0 → B0 is compact and T: A1 → B1 is compact (or T: A1 → B1 is bounded and, then given any θ and q with 0 < θ < 1 and 0 < q⩽ ∞, it follows that T: (A0, A1)0,q → (B0, B1)0,q, is also compact. Here (A0, A1)0,q and (B0, B1)0,q are the usual real interpolation spaces.