Rad HAZU, Matematičke znanosti, Vol. 23 (2019), 1-11.

REARRANGING ABSOLUTELY CONVERGENT WELL-ORDERED SERIES IN BANACH SPACES

Vedran Čačić, Marko Doko and Marko Horvat

Max Planck Institute for Software Systems, 67663 Kaiserslautern, Germany
e-mail: mdoko@mpi-sws.org

Department of Mathematics, University of Zagreb, 10000 Zagreb, Croatia
e-mail: mhorvat@math.hr

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.

2010 Mathematics Subject Classification.   03E10, 40A05.

Key words and phrases.   Well-ordered series, summability, absolute convergence, reordering, Banach spaces, ordinals.

DOI: https://doi.org/10.21857/yq32oh4qd9

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