On uniformly smoothing stochastic operators

Wojciech Bartoszek

Commentationes Mathematicae Universitatis Carolinae (1995)

  • Volume: 36, Issue: 1, page 203-206
  • ISSN: 0010-2628

Abstract

top
We show that a stochastic operator acting on the Banach lattice L 1 ( m ) of all m -integrable functions on ( X , 𝒜 ) is quasi-compact if and only if it is uniformly smoothing (see the definition below).

How to cite

top

Bartoszek, Wojciech. "On uniformly smoothing stochastic operators." Commentationes Mathematicae Universitatis Carolinae 36.1 (1995): 203-206. <http://eudml.org/doc/247713>.

@article{Bartoszek1995,
abstract = {We show that a stochastic operator acting on the Banach lattice $L^1(m)$ of all $m$-integrable functions on $(X,\,\mathcal \{A\})$ is quasi-compact if and only if it is uniformly smoothing (see the definition below).},
author = {Bartoszek, Wojciech},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {stochastic operators; quasi-compact; stochastic operator; Banach lattice; quasi-compact; uniformly smoothing},
language = {eng},
number = {1},
pages = {203-206},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On uniformly smoothing stochastic operators},
url = {http://eudml.org/doc/247713},
volume = {36},
year = {1995},
}

TY - JOUR
AU - Bartoszek, Wojciech
TI - On uniformly smoothing stochastic operators
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1995
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 36
IS - 1
SP - 203
EP - 206
AB - We show that a stochastic operator acting on the Banach lattice $L^1(m)$ of all $m$-integrable functions on $(X,\,\mathcal {A})$ is quasi-compact if and only if it is uniformly smoothing (see the definition below).
LA - eng
KW - stochastic operators; quasi-compact; stochastic operator; Banach lattice; quasi-compact; uniformly smoothing
UR - http://eudml.org/doc/247713
ER -

References

top
  1. Bartoszek W., On quasi-compactness and invariant measures of Markov operators on C ( X ) , Bull. Acad. Polon. Sci. 34 (1986), 69-72. (1986) Zbl0614.47030MR0850316
  2. Bartoszek W., Asymptotic periodicity of the iterates of positive contractions on Banach lattices, Studia Math. XCI (1988), 179-188. (1988) MR0985720
  3. Bartoszek W., On the asymptotic behaviour of iterates of positive linear operators, Die Suid-Afrikaanse Wiskundevereniging Mededelings 25:1 (1993), 48-78. (1993) 
  4. Komorník J., Asymptotic decomposition of smoothing positive operators, Acta Universitatis Carolinae (1989), 30:2 77-81. (1989) MR1046450
  5. Komorník J., Lasota A., Asymptotic decomposition of Markov operators, Bull. Acad. Polon. Sci. 35 no. 5-6 (1987), 321-327. (1987) MR0919219
  6. Lasota A., Mackey M.C., Probabilistic Properties of Deterministic Systems, Cambridge University Press, Cambridge, 1985. Zbl0606.58002MR0832868
  7. Sine R., A mean ergodic theorem, Proc. Amer. Math. Soc. 24 (1970), 438-439. (1970) Zbl0191.42204MR0252605

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.