Mean lower bounds for Markov operators

• Autorzy: Eduard Emel'yanov , Manfred Wolff
• Języki publikacji: EN

Abstrakty

EN

Let T be a Markov operator on an L¹-space. We study conditions under which T is mean ergodic and satisfies dim Fix(T) < ∞. Among other things we prove that the sequence $(n^{-1} ∑_{k=0}^{n-1} T^k)ₙ$ converges strongly to a rank-one projection if and only if there exists a function 0 ≠ h ∈ L¹₊ which satisfies $lim_{n→∞} ||(h - n^{-1} ∑_{k=0}^{n-1} T^k f)₊|| = 0$ for every density f. Analogous results for strongly continuous semigroups are given.

Kategorie tematyczne

• 47A35: Ergodic theory
• 37A30: Ergodic theorems, spectral theory, Markov operators

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2004
• Tom: 83
• Numer: 1
• Strony: 11-19

Daty

wydano

2004

Twórcy

autor

Eduard Emel'yanov

• Sobolev Institute of Mathematics, Akad. Koptyug pr. 4, 630090 Novosibirsk, Russia

autor

Manfred Wolff

• Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, D-72076 Tübingen, Germany

Identyfikatory

DOI

10.4064/ap83-1-2