Example of a mean ergodic L¹ operator with the linear rate of growth

• Autorzy: Wojciech Kosek
• Języki publikacji: EN

Abstrakty

EN

The rate of growth of an operator T satisfying the mean ergodic theorem (MET) cannot be faster than linear. It was recently shown (Kornfeld-Kosek, Colloq. Math. 98 (2003)) that for every γ > 0, there are positive L¹[0,1] operators T satisfying MET with $lim_{n→ ∞}||Tⁿ||/n^{1-γ} = ∞$. In the class of positive L¹ operators this is the most one can hope for in the sense that for every such operator T, there exists a γ₀ > 0 such that $lim sup||Tⁿ||/n^{1-γ₀} = 0.$ In this note we construct an example of a nonpositive L¹ operator with the highest possible rate of growth, that is, $lim sup_{n → ∞}||Tⁿ||/n > 0$.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2011
• Tom: 124
• Numer: 1
• Strony: 15-22

Daty

wydano

2011

Twórcy

autor

Wojciech Kosek

• Colorado Technical University, 4435 North Chestnut Street, Colorado Springs, CO 80907, U.S.A.

Identyfikatory

DOI

10.4064/cm124-1-2