Asymptotic periodicity of Markov operators of signed measures. (English) Zbl 0758.47033

Komorník, Jozef; Thomas, Erik G. F.

Math. Bohem. 116, No. 2, 174-180 (1991).

A criterion for asymptotic periodicity of Markov operators on \(L^ 1\) was established by the first author [Tôhoku Math J. 38, 15-27 (1986; Zbl 0578.47020) and Bull. Pol. Acad. Sci., Math. 35, 321-327 (1987; Zbl 0642.47026)]. In this paper, a generalization of the above result is provided for a quasi-constructive Markov operator on any band in the space of signed measures on a \(\sigma\)-algebra.

Reviewer: W.A.Feldman (Fayetteville)

MSC:

47B60	Linear operators on ordered spaces
28A33	Spaces of measures, convergence of measures
46E27	Spaces of measures

Keywords:

asymptotic periodicity of Markov operators; quasi-constructive Markov operator; band; space of signed measures on a \(\sigma\)-algebra

Citations:

Zbl 0578.47020; Zbl 0642.47026