Skip to main content
Log in

Uniform convergence of operators onL and similar spaces

  • Published:
Mathematische Zeitschrift Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Ando, T.: Convergent sequences of finitely additive measures. Pacific J. Math.11, 395–404 (1961)

    Google Scholar 

  2. Ando, T.: Invariante Masse positiver Kontraktionen aufC(X). Studia Math.31, 777–788 (1969)

    Google Scholar 

  3. Bourbaki, N.: Topologie Générale, chap. 1 et 2, 4e ed. Paris: Hermann 1965; chap. 9, 2e ed. Paris: Hermann 1958

    Google Scholar 

  4. Davies, E.B.: One-Parameter Semigroups. London-New York: Academic Press 1980

    Google Scholar 

  5. Dean, D.W.: Schauder decompositions in (m). Proc. Amer. Math. Soc.18, 619–623 (1967)

    Google Scholar 

  6. Dunford, N.: Spectral theory I, Convergence to projections. Trans. Amer. Math. Soc.54, 185–217 (1943)

    Google Scholar 

  7. Dunford, N., Schwartz, J.T.: Linear Operators, Part I: General Theory. New York: Wiley 1958

    Google Scholar 

  8. Grothendieck, A.: Sur les applications linéaires faiblement compactes d'espaces du typeC(K). Canad. J. Math.5, 129–173 (1953)

    Google Scholar 

  9. Hille, E., Phillips, R.S.: Functional Analysis and Semi-Groups. Providence, R. I.: Amer. Math. Soc. 1957

    Google Scholar 

  10. Josefson, B.: Weak sequential convergence in the dual of a Banach space does not imply norm convergence. Ark. Mat.13, 79–89 (1975)

    Google Scholar 

  11. Kishimoto, A., Robinson, D.W.: Subordinate semigroups and order properties. J. Austral. Math. Soc. Ser. A31, 59–76 (1981)

    Google Scholar 

  12. Lindenstrauss, J., Tzafriri, L.: Classical Banach Spaces. Lecture Notes in Math.338. Berlin-Heidelberg-New York: Springer 1973

    Google Scholar 

  13. Lotz, H.P.: Uniform ergodic theorems for Markov operators onC(X). Math. Z.178, 145–156 (1981)

    Google Scholar 

  14. Lotz, H.P.: Quasi-kompakte positive Kontraktionen aufC(X). Semesterbericht Funktionalanalysis, Tübingen, Wintersemester 1981/82, pp. 139–147

  15. Lotz, H.P.: Tauberian theorems for operators onL and similar spaces. In: Functional Analysis, Surveys and Recent Results III. K.-D. Bierstedt and B. Fuchssteiner (eds.), 117–133. Amsterdam: Elsevier Science Publishers B.V. (North-Holland) 1984

    Google Scholar 

  16. Nissenzweig, A.:w * sequential convergence. Israel J. Math.22, 266–272 (1975)

    Google Scholar 

  17. Schaefer, H.H.: Topological Vector Spaces. New York-London: Macmillan 1966

    Google Scholar 

  18. Schaefer, H.H.: Banach Lattices and Positive Operators. Berlin-Heidelberg-New York: Springer 1974

    Google Scholar 

  19. Seever, G.L.: Measures onF-spaces. Trans. Amer. Math. Soc.133, 267–280 (1968)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Meinem verehrten Lehrer Helmut H. Schaefer zum 60. Geburtstag in Dankbarkeit gewidmet

The author is grateful to the Deutsche Forschungsgemeinschaft for support during his stag as Visiting Professor at the Universität Tübingen.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lotz, H.P. Uniform convergence of operators onL and similar spaces. Math Z 190, 207–220 (1985). https://doi.org/10.1007/BF01160459

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01160459

Keywords

Navigation