Abstract
Following Bermúdez et al. [5], we study the rate of growth of the norms of the powers of a linear operator, under various resolvent conditions or Cesàro boundedness assumptions. In Hilbert spaces, we prove that if T satisfies the Kreiss condition, ‖Tn‖=O(n/logn); if T is absolutely Cesàro bounded, ‖Tn‖=O(n1/2−ε) for some ε>0 (which depends on T); if T is strongly Kreiss bounded, then ‖Tn‖=O((logn)κ) for some κ>0. We show that a Kreiss bounded operator on a reflexive space is Abel ergodic, and its Cesàro means of order α converge strongly when α>1.
Original language | English |
---|---|
Article number | 124035 |
Journal | Journal of Mathematical Analysis and Applications |
Volume | 487 |
Issue number | 2 |
DOIs | |
State | Published - 15 Jul 2020 |
Keywords
- Abel boundedness
- Cesàro boundedness
- Kreiss resolvent condition
- Mean ergodicity
- Power-boundedness
ASJC Scopus subject areas
- Analysis
- Applied Mathematics