Some compactness results in real interpolation for families of Banach spaces

The paper shows that, if the operator T: A(gamma) --> B(gamma) is compact f or almost every gamma epsilon Gamma, then T: F((A) over bar) --> F((B) over bar) is compact when F((X) over bar) = (X)(K)(S) or F((X) over bar)=(X)(J) (S) is the interpolation functor constructed for infinite families of Banac h spaces and S satisfies certain conditions.