The Maximal Subspace for Generation of ( a , k ) -Regularized Families

Abstract

Let $A$ be a linear operator in a Banach space $X$. We define a subspace of $X$ and a norm such that the part of $A$ in such subspace generates an ($a$, $k$)-regularized resolvent family. This space is maximal-unique in a suitable sense and nontrivial, under certain conditions on the kernels $a$ and $k$.