A strengthened Orlicz–Pettis theorem via Itô–Nisio

نویسندگان

چکیده

Abstract In this note, we deduce a strengthening of the Orlicz–Pettis theorem from Itô–Nisio theorem. The argument shows that given any series in Banach space which is not summable (or more generally unconditionally summable), can construct (coarse-grained) subseries with property that—under some appropriate notion “almost all”—almost all further thereof fail to be weakly summable. Moreover, by Hoffmann–Jørgensen allows us replace ‘weakly summable’ ‘ $$\tau$$ τ -weakly for topologies weaker than weak topology. A treatment admissible given.

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ژورنال

عنوان ژورنال: Annals of Functional Analysis

سال: 2023

ISSN: ['2639-7390', '2008-8752']

DOI: https://doi.org/10.1007/s43034-022-00225-1