2024/08/16 by Jochen Glück, Glück, Jochen, Patrick Hermle +3
Mathematics · #46B42 #47B65 #47D03 #47D06 #Advanced Banach Space Theory #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Dynamics and Fractals #Spectral Theory (math.SP) #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.2408.08961
openalex publication_date 2024/08/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider a bounded representation T of a commutative semigroup S on a Banach space and analyse the relation between three concepts: (i) properties of the unitary spectrum of T, which is defined in terms of semigroup characters on S; (ii) uniform mean ergodic properties of T; and (iii) quasi-compactness of T. We use our results to generalize the celebrated Niiro-Sawashima theorem to semigroup representations and, as a consequence, obtain the following: if a positive and bounded semigroup representation on a Banach lattice is uniformly mean ergodic and has finite-dimensional fixed space, then it is quasi-compact.