Zeitschrift für Analysis und ihre Anwendungen
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Published online: 1998-12-31
Orlicz-Pettis Theorems for Multiplier Convergent SeriesC. Swartz and C. Stuart (1) New Mexico State University, Las Cruces, USA
(2) Eastern New Mexico State University, Portales, USA
Orlicz-Pettis theorems have been established for multiplier convergent series where the multipliers come from $c_0$ or $l^p (0 < p < \infty)$. We show that these results as well as the classical Orlicz-Pettis theorem are corollaries of a general result based on the fact that all of these multiplier spaces have the canonical unit vectors as a Schauder basis.
Keywords: Orlicz-Pettis theorems, multiplier convergent series
Swartz C., Stuart C.: Orlicz-Pettis Theorems for Multiplier Convergent Series. Z. Anal. Anwend. 17 (1998), 805-811. doi: 10.4171/ZAA/851