Mathematische Zeitschrift

, Volume 207, Issue 1, pp 109–120 | Cite as

Quasi-compactness of dominated positive operators andCo-semigroups

  • Josep Martinez
  • José M. Mazón
Article

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Aliprantis, C.D., Burkinshaw, O.: Positive compact operators on Banach lattices, Math. Z.174, 289–298 (1980)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Aliprantis, C.D., Burkinshaw, O.: Positive Operators, New York, Academic Press 1985MATHGoogle Scholar
  3. 3.
    Andreu, F., Mazón, J.M.: On the boundary spectrum of dominatedC o-semigroups. Semigroup Forum38, 129–139 (1989)MATHMathSciNetGoogle Scholar
  4. 4.
    Arendt, W.: On theo-spectrum of regular operators and the spectrum of measures. Math. Z.178, 271–287 (1981)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Arendt, W., Sourour, A.R.: Perturbation of regular operator and the order essential spectrum. Indagationes Math.89, 109–122 (1986)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Brunel, A., Revuz, D.; Quelques applications probabilistes de la quasi-compacité. Ann. Inst. Henri Poincaré10, 301–337 (1974)MathSciNetGoogle Scholar
  7. 7.
    Caselles, V.: On the periferical spectrum of positive operators. Isr. J. Math.58, 144–160 (1987)MATHMathSciNetGoogle Scholar
  8. 8.
    Clément, Ph. et al.: One-Parameter Semigroups. New York: North-Holland 1987MATHGoogle Scholar
  9. 9.
    Dodds, P.G., Fremlin, D.H.: Compact operators in Banach lattices. Isr. J. Math.34, 287–320 (1979)MATHMathSciNetGoogle Scholar
  10. 10.
    Greiner, G., Voigt, J., Wolff, M.: On the spectral bound of the generator of semigroups of positive operators. J. Oper. Theory5, 245–256 (1981)MATHMathSciNetGoogle Scholar
  11. 11.
    Greiner, G., Nagel, R.: Growth of cell populations via one-parameter semigroups of positive operators. In: Mathematics Applied to Science, New York Academic Press 1988Google Scholar
  12. 12.
    Heijmans, H.J.A.M.: Structured populations, linear semigroups and positivity. Math. Z.191, 599–617 (1986)MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Heuser, H.G.: Functional Analysis, New York: Yohn Wiley 1982MATHGoogle Scholar
  14. 14.
    Krengel, U.: Ergodic Theorems. De Gruyter 1985Google Scholar
  15. 15.
    Kryloff, N., Bogoliuboff, N.: Sur les probabilites en chaine, C.R. Acad. Sci. (Paris)204, 1368–1389 (1937)Google Scholar
  16. 16.
    Lin, M.: On the uniform ergodic theorem. Proc. Am. Math. Soc.43, 337–340 (1974)MATHCrossRefGoogle Scholar
  17. 17.
    Lin, M.: Quasi-compactness and uniform ergodicity of Markov operators, Ann. Inst. Henri Poincaré11, 345–354 (1975)MATHGoogle Scholar
  18. 18.
    Lin, M.: Quasi-compactness and uniform ergodicity of positive operators. Isr. J. Math.29, 309–311 (1978)MATHGoogle Scholar
  19. 19.
    Lotz, H.P.: Uniform ergodic theorems for Markov operators onC(X). Math. Z.178, 145–156 (1981)CrossRefMathSciNetGoogle Scholar
  20. 20.
    Lotz, H.P.: Positive linear operators onL p and Doeblin condition. In: R. Nagel, U. Schlotterbeck, M. Wolff (eds.), Aspects of Positivity in Functional Analysis. New York: North-Holland 1986Google Scholar
  21. 21.
    Nagel, R. (ed.): One-Parameter Semigroups of Positive Operators. (Lect. Notes Math, Vol.1184) Berlin Heidelberg New York: Sprigner 1986MATHGoogle Scholar
  22. 22.
    O'Brien, R.E.: Contraction semigroups, stabilization, and mean ergodic theorem, Proc. Am. Math. Soc.71, 89–94 (1978)MATHCrossRefMathSciNetGoogle Scholar
  23. 23.
    Pagter, B. de, Schep, A.R.: Measures of non-compactness of positive operators in Banach lattices, J. Funct. Anal.78, 31–55 (1988)MATHCrossRefMathSciNetGoogle Scholar
  24. 24.
    Schaefer, H.H., Banach Lattices and Positive Operators, Berlin Heidelberg New York: Springer 1974MATHGoogle Scholar
  25. 25.
    Schaefer, H.H.: On theo-spectrum of order bounded operators. Math. Z.154, 79–84 (1977)MATHCrossRefMathSciNetGoogle Scholar
  26. 26.
    Webb, G.F.: An operator-theoretic formulation of asynchronous exponential growth. Trans. Am. Math. Soc.303, 751–763 (1987)MATHCrossRefMathSciNetGoogle Scholar
  27. 27.
    Weis, L., Wolff, M.: On the essential spectrum of operators onL 1. Semesterbericht Funk. Anal. Tuebingen 103–112 (Sommersemester 1984)Google Scholar
  28. 28.
    Yosida, K., Kakutani, S.: Operator-theoretical treatment of Markoff's process and mean ergodic theorem. Ann. Math.42, 188–228 (1941)CrossRefMathSciNetGoogle Scholar
  29. 29.
    Zaanen, A.C.: Riesz Spaces II, New York: North-Holland 1983MATHGoogle Scholar

Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • Josep Martinez
    • 1
  • José M. Mazón
    • 1
  1. 1.Departamento de Análisis MatemáticoUniversitat de ValenciaBurjassotSpain

Personalised recommendations