Interpolation of some properties of operators acting in families of Banach spaces

Abstract

Let $T$ be an operator acting from family $A_t$ into family $B_t$, possessing some properties like compactness, positive measure of noncompcatness or being limited when it acts from $A_t$ into $B_t$ for $t$ from some positive measure subset. In the case when one of the families is constant some results are presentes about the behaviour of $T$ like an operator acting from $A$ into $B$, where $A$ and $B$ are interpolation spaces constructed for the families $A_t$ and $B_t$. It is shown how some geometric properties are inherited by interpolation spaces.