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Theorems of the Orlicz-Pettis-type for locally convex spaces

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Abstract

For a dual pair <E,F> we determine the finest <E,F> -polar topology on E which has the same subfamily-summable (respectively bounded multiplier summable) families as the weak topology б(E,F). It is shown that these characterizations contain most of the known theorems of the ORLICZ-PETTIS-type for locally convex spaces and also several new results of this type. Some applications to spaces of functions and operators are given.

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  1. Mathematisches Institut der Universität München, Theresienstr. 39, D 8000, München 2

    Peter Dierolf

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  1. Peter Dierolf
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Dierolf, P. Theorems of the Orlicz-Pettis-type for locally convex spaces. Manuscripta Math 20, 73–94 (1977). https://doi.org/10.1007/BF01181241

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