关键词: 准Banach-Steinhaus性质, Orlicz-Pettis定理, 乘数收敛, 序列空间

Abstract:

Depending only upon the intrinsic properties of a sequence space λ, the authors endow a locally convex topology T_Β on λ-multiplier convergent series space X(λ) and obtain that (X(λ), T_Β) 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