Let \(\bar A=(A_ 0,A_ 1)\) and \(\bar B=(B_ 0,B_ 1)\) be Banach couples and suppose that T: \(A_ i\to B_ i\), is a compact operator, \(i=1,2\). The authors prove that, for all F maximal or minimal Aronszajn- Gagliardo interpolation functor, \(T: F(\bar A)\to F(\bar B)\) is compact. The result applies, in particular, to the real method of interpolation, and therefore provides an extension of a well known theorem of \textit{K. Hayakawa} [J. Math. Soc. Japan 21, 189-199 (1969; Zbl 0181.137)].