Interpolating Some Classes of Operators between Families - Suárez, Alexi Quevedo (Communications in Mathematics and Applications, 2014)
Many operator ideals (single operator ideals and chains, see inside) possess the strong property of interpolation for the J and K methods of Lions-Peetre, Sparr, Fernandez and Cobos-Peetre. That is, let I be one of the ideals considered here, let A and B be interpolation families and T : A→B a bounded linear operator then, the interpolated operator T_J;K : J(A)→ K(B) belongs to I if and only if the induced operator T_JS from the intersection space J (A) into the sum space S(B) belongs to I.