Operators with an ergodic power

Teresa Bermúdez; Manuel González; Mostafa Mbekhta

Studia Mathematica (2000)

  • Volume: 141, Issue: 3, page 201-208
  • ISSN: 0039-3223

Abstract

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We prove that if some power of an operator is ergodic, then the operator itself is ergodic. The converse is not true.

How to cite

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Bermúdez, Teresa, González, Manuel, and Mbekhta, Mostafa. "Operators with an ergodic power." Studia Mathematica 141.3 (2000): 201-208. <http://eudml.org/doc/216779>.

@article{Bermúdez2000,
abstract = {We prove that if some power of an operator is ergodic, then the operator itself is ergodic. The converse is not true.},
author = {Bermúdez, Teresa, González, Manuel, Mbekhta, Mostafa},
journal = {Studia Mathematica},
keywords = {Cesàro means; ergodic},
language = {eng},
number = {3},
pages = {201-208},
title = {Operators with an ergodic power},
url = {http://eudml.org/doc/216779},
volume = {141},
year = {2000},
}

TY - JOUR
AU - Bermúdez, Teresa
AU - González, Manuel
AU - Mbekhta, Mostafa
TI - Operators with an ergodic power
JO - Studia Mathematica
PY - 2000
VL - 141
IS - 3
SP - 201
EP - 208
AB - We prove that if some power of an operator is ergodic, then the operator itself is ergodic. The converse is not true.
LA - eng
KW - Cesàro means; ergodic
UR - http://eudml.org/doc/216779
ER -

References

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  2. [2] T. Bermúdez, M. González and M. Mbekhta, Local ergodic theorems, Extracta Math. 13 (1997), 243-248. 
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  7. [7] N. Dunford, Spectral theory I. Convergence to projections, Trans. Amer. Math. Soc. 54 (1943), 185-217. Zbl0063.01185
  8. [8] U. Krengel, Ergodic Theorems, de Gruyter Stud. Math. 6, Berlin, 1985. 
  9. [9] K. B. Laursen and M. Mbekhta, Operators with finite chain length and the ergodic theorem, Proc. Amer. Math. Soc. 123 (1995), 3443-3448. Zbl0849.47008
  10. [10] M. Mbekhta et J. Zemánek, Sur le théorème ergodique uniforme et le spectre, C. R. Acad. Sci. Paris Sér. I Math. 317 (1993), 1155-1158. 
  11. [11] M. Radjabalipour, Decomposable operators, Bull. Iranian Math. Soc. 9 (1978), 1L-49L. Zbl0696.47032
  12. [12] R. Sine, A note on the ergodic properties of homeomorphisms, Proc. Amer. Math. Soc. 57 (1976), 169-172. Zbl0333.54027
  13. [13] A. C. Taylor and D. C. Lay, Introduction to Functional Analysis, 2nd ed., Wiley, New York, 1980. Zbl0501.46003
  14. [14] H.-D. Wacker, Über die Verallgemeinerung eines Ergodensatzes von Dunford, Arch. Math. (Basel) 44 (1985), 539-546. Zbl0555.47008

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