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 $\mathcal{I}$ be one of the ideals considered here, let $\bar{A}$ and $\bar{B}$ be interpolation families and $T : \bar{A}→\bar{B}$ a bounded linear operator then, the interpolated operator $T_{J;K} : J(\bar{A})→ K(\bar{B})$ belongs to $\mathcal{I}$ if and only if the induced operator $T_{\mathcal{JS}}$ from the intersection space $\mathcal{J} (\bar{A})$ into the sum space $\mathcal{S}(B)$ belongs to $\mathcal{I}$.
Keywords: Real methods of interpolation between families; Operator ideals