Interpolation orbit functors and reiteration theorems
In the paper under review, the author uses certain ideals operators to study interpolation orbit functors from couples of weighted \(\ell^p\) or \(c_0\) spaces to the class of regular finite dimensional couples. The author shows that the abstract \(J\)-method of interpolation has an orbital description which is used to study interpolation orbit functors from the couples of weighted \(\ell^p\) or \(c_0\) spaces. It is proved that on the class of regular finite dimensional couples these functors coincide isometrically with a certain interpolation functor generated by a product ideal \(Q_{q_0} \otimes Q_{q_1}\) of \(q_j\)-nuclear operators \((1/p_j+ 1/q_j=1\), \(j=0,1)\). Reiteration theorems of the form \({\mathcal F}\{G_{\theta_0,p}, G_{\theta_{1,p}}\} =G_{\theta,p}\) for certain interpolation functors \({\mathcal F}\) and orbit functors \(G_{\theta,p}\) of the sequence \(\{2^{n\theta}\}\) and the couple \((\ell^p,\ell^p (2^{-n}))\) are also given.
scientific article; zbMATH DE number 1540338
scientific article