An abstract Orlics-Pettis theorem and applications


  • Li Ronglu Harbin Institute of Technology.
  • Charles Swartz New Mexico State University.



Topological vector space, locally convex spaces, convergent series, operators, espacios vectoriales topológicos, espacios localmente convexos, series convergentes, operadores.


In this paper we establish two abstract versions of the classical Orlicz-Pettis Theorem for multiplier convergent series. We show that these abstract results yield known versions of the Orlicz-Pettis Theorem for locally convex spaces as well as versions for operator valued series. We also give applications to vector valued measures and spaces of continuous functions.

Author Biographies

Li Ronglu, Harbin Institute of Technology.

Department of Mathematics.

Charles Swartz, New Mexico State University.

Department of Mathematics.


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How to Cite

L. Ronglu and C. Swartz, “An abstract Orlics-Pettis theorem and applications”, Proyecciones (Antofagasta, On line), vol. 27, no. 2, pp. 155-169, May 2017.