2025/12/01 by Mugnolo, Delio
Mathematics · #Advanced Banach Space Theory #Nonlinear Differential Equations Analysis #Advanced Operator Algebra Research
paper · doi:10.48550/arxiv.2512.01397
In analogy to a recent result by V. Fonf, M. Lin, and P. Wojtaszczyk, we prove the following characterizations of a Banach space X with a basis. (i) X is finite-dimensional if and only if every bounded, uniformly continuous, mean ergodic semigroup on X is uniformly mean ergodic. (ii) X is reflexive if and only if every bounded strongly continuous semigroup is mean ergodic if and only if every bounded uniformly continuous semigroup on X is mean ergodic.