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Rad Hrvatske akademije znanosti i umjetnosti. Matematičke znanosti, No. 538=23, 2019.

Original scientific paper

https://doi.org/10.21857/yq32oh4qd9

Rearranging absolutely convergent well-ordered series in Banach spaces

Vedran Čačić ; Department of Mathematics, University of Zagreb, 10000 Zagreb, Croatia
Marko Doko ; Max Planck Institute for Software Systems, 67663 Kaiserslautern, Germany
Marko Horvat ; Department of Mathematics, University of Zagreb, 10000 Zagreb, Croatia

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Abstract

We identify a general reordering principle for well-ordered series in Banach spaces. We prove that for every absolutely convergent wellordered series indexed by a countable ordinal, if the series is rearranged according to any countable ordinal, then the absolute convergence and the sum of the series remain unchanged.

Keywords

Well-ordered series: summability; absolute convergence; reordering; Banach spaces; ordinals.

Hrčak ID:

225226

URI

https://hrcak.srce.hr/225226

Publication date:

17.9.2019.

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