Generalizations of the Orlicz - Pettis theorem


  • Christopher Stuart New Mexico State University.
  • Charles Swartz New Mexico State University.



The Orlicz-Pettis Theorem for locally convex spaces asserts that a series in the space which is subseries convergent in the weak topology is actually subseries convergent in the original topology of the space. A subseries convergent series can be viewed as a multiplier convergent series where the terms of the series are multiplied by elements of the scalar sequence space m0 of sequences with finite range. In this paper we show that the conclusion of the Orlicz-Pettis Theorem holds (and can be strengthened) if the multiplier space m0 is replaced by a sequence space with the signed weak gliding hump property.

Author Biographies

Christopher Stuart, New Mexico State University.

Department of Mathematical Sciences.

Charles Swartz, New Mexico State University.

Department of Mathematical Sciences.


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How to Cite

C. Stuart and C. Swartz, “Generalizations of the Orlicz - Pettis theorem”, Proyecciones (Antofagasta, On line), vol. 24, no. 1, pp. 37-48, Apr. 2017.