2019/12/23 by Abdelaziz Tajmouati, Tajmouati, Abdelaziz, Fatih Barki +1
Mathematics · #Nonlinear Differential Equations Analysis #Advanced Banach Space Theory #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.1912.10947
Let \T(t)\t≥ 0 be a C0-semigroup of bounded linear operators on the Banach space X into itself and let A be their infinitesimal generator. In this paper, we show that if T(t) is uniformly ergodic, then A does not have the single valued extension property, which implies that A must have a nonempty interior of the point spectrum. Furthermore, we introduce the local mean ergodic for C0-semigroup T(t) at a vector x∈ X and we establish some conditions implying that T(t) is a local mean ergodic at x.