On the local Ritt resolvent condition

Abstract

. Let T be a linear bounded operator on a complex Banach space X . In this paper, we introduce a local version of the Ritt resolvent condition [ LR ] for Banach space operators T . We start by showing that this concept is weaker than the classical Ritt condition [ R ] . We prove that, for operators with single-valued extension property (SVEP), estimate [ LR ] extends, with a larger constant, to some sector K δ . Moreover, by extending some Ritt’s theorems to the local case for operators with the SVEP, several characterizations of the local sublinear decay of T n − T n + 1 have been established.