On a result of Peetre about interpolation of operator spaces
For quasi-normed operator ideals \({\mathcal J}\), the authors find conditions on couples of Banach spaces (such as regularity, quasi-linearizability), or on \({\mathcal J}\) (such as injectivity or surjectivity), and on the interpolation parameters, that allow to establish inclusion relations between \({\mathcal J}(A,B)\) and real interpolated spaces of couples \(({\mathcal J}(A,B_0),{\mathcal J}(A,B_1))\) or \(({\mathcal J}(A_0,B),{\mathcal J}(A_1,B))\)), when \(B\) is an intermediate space with respect to \((B_0,B_1)\) or \(A\) is an intermediate space with respect to \((A_0,A_1)\), respectively. They apply their results to identify some interpolated spaces between couples of spaces of operators and of tensor products, in the direction of previous results due to Kouba and to Ovchinnikov.
scientific article; zbMATH DE number 1563893