Acta mathematica scientia,Series A ›› 2009, Vol. 29 ›› Issue (5): 1167-1174.

• Articles • Previous Articles     Next Articles

A Class of Multiplier Convergent Series Spaces

  

  1. Department of Mathematics, Harbin Institute of Technology, Harbin 150001
  • Received:2007-08-20 Revised:2008-11-25 Online:2009-10-25 Published:2009-10-25

Abstract:

Depending only upon the intrinsic properties of a sequence space λ, the authors endow a locally convex topology TΒ on λ-multiplier convergent series space X(λ) and obtain that (X(λ), TΒ) is an AK-space and has sequentially completeness and Banach-Steinhaus properties. In particular, the authors give a generalization of the Orlicz-Pettis theorem for the series in X(λ).

Key words: Quasi Banach-Steinhaus property, Orlicz-Pettis theorem, Multiplier convergent, Sequence space

CLC Number: 

  • 46A03
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