Uniform ergodic theorems for semigroup representations

Autor:	Glück, Jochen, Hermle, Patrick, Kreidler, Henrik
Rok vydání:	2024
Předmět:	Mathematics - Functional Analysis Mathematics - Spectral Theory 47D03 47D06 47B65 46B42
Druh dokumentu:	Working Paper
Popis:	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. Comment: 33 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2408.08961 Zobrazit plný text záznamu View this record from Arxiv