A series whose sum range is an arbitrary finite set

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dc.creatorWojtaszczyk, Jakub Onufry
dc.date2008-03-04
dc.date.accessioned2026-07-07T09:24:33Z
dc.date.available2026-07-07T09:24:33Z
dc.descriptionIn finitely-dimensional spaces the sum range of a series has to be an affine subspace. It is long known this is not the case in infinitely dimensional Banach spaces. In particular in 1984 M.I. Kadets and K. Wozniakowski obtained an example of a series the sum range of which consisted of two points, and asked whether it is possible to obtain more than two, but finitely many points. This paper answers the question positively, by showing how to obtain an arbitrary finite set as the sum range of a series in any infinitely dimensional Banach space.
dc.description21 pages
dc.identifierhttps://arxiv.org/abs/0803.0415
dc.identifierhttp://arxiv.org/abs/0803.0415
dc.identifierStudia Mathematica 171 (3) (2005), pp. 261-281
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/156135
dc.subjectFunctional Analysis
dc.subject46B15
dc.titleA series whose sum range is an arbitrary finite set
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