| Title:
|
On uniformly smoothing stochastic operators (English) |
| Author:
|
Bartoszek, Wojciech |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
36 |
| Issue:
|
1 |
| Year:
|
1995 |
| Pages:
|
203-206 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We show that a stochastic operator acting on the Banach lattice $L^1(m)$ of all $m$-integrable functions on $(X,\,\Cal A)$ is quasi-compact if and only if it is uniformly smoothing (see the definition below). (English) |
| Keyword:
|
stochastic operators |
| Keyword:
|
quasi-compact |
| MSC:
|
47A35 |
| MSC:
|
47B07 |
| MSC:
|
47B38 |
| MSC:
|
47B55 |
| MSC:
|
47B65 |
| MSC:
|
47D07 |
| idZBL:
|
Zbl 0843.47018 |
| idMR:
|
MR1334427 |
| . |
| Date available:
|
2009-01-08T18:17:03Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118745 |
| . |
| Reference:
|
[B1] Bartoszek W.: On quasi-compactness and invariant measures of Markov operators on $C(X)$.Bull. Acad. Polon. Sci. 34 (1986), 69-72. Zbl 0614.47030, MR 0850316 |
| Reference:
|
[B2] Bartoszek W.: Asymptotic periodicity of the iterates of positive contractions on Banach lattices.Studia Math. XCI (1988), 179-188. MR 0985720 |
| Reference:
|
[B3] Bartoszek W.: On the asymptotic behaviour of iterates of positive linear operators.Die Suid-Afrikaanse Wiskundevereniging Mededelings 25:1 (1993), 48-78. |
| Reference:
|
[K] Komorník J.: Asymptotic decomposition of smoothing positive operators.Acta Universitatis Carolinae (1989), 30:2 77-81. MR 1046450 |
| Reference:
|
[KL] Komorník J., Lasota A.: Asymptotic decomposition of Markov operators.Bull. Acad. Polon. Sci. 35 no. 5-6 (1987), 321-327. MR 0919219 |
| Reference:
|
[LM] Lasota A., Mackey M.C.: Probabilistic Properties of Deterministic Systems.Cambridge University Press, Cambridge, 1985. Zbl 0606.58002, MR 0832868 |
| Reference:
|
[S] Sine R.: A mean ergodic theorem.Proc. Amer. Math. Soc. 24 (1970), 438-439. Zbl 0191.42204, MR 0252605 |
| . |
