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. © 2012 Edgardo Alvarez-Pardo and Carlos Lizama.