A unified approach to compatibility theorems on invertible interpolated operators

Abstract

We prove the stability of isomorphisms between Banach spaces generated by interpolation methods introduced by Cwikel-Kalton-Milman-Rochberg which includes, as special cases, the real and complex methods up to equivalence of norms and also the so-called $\pm$ or $G_1$ and $G_2$ methods defined by Peetre and Gustavsson-Peetre. This result is used to show the existence of solution of certain operator analytic equation. A by product of these results is a more general variant of the Albrecht-Müller result which states that the interpolated isomorphisms satisfy uniqueness-of-inverses between interpolation spaces. We show applications for positive operators between Calderón function lattices. We also derive connections between the spectrum of interpolated operators.

25 pages

Cited by in corpus (1)

• A discrete framework for the interpolation of Banach spaces