Geodesic
A series whose sum range is an arbitrary finite set
Jakub Onufry Wojtaszczyk1
1Department of Mathematics, Computer Science and Mechanics University of Warsaw Banacha 2 02-097 Warszawa, Poland
Studia Mathematica, Tome 171 (2005) no. 3, pp. 261-281
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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In finite-dimensional spaces the sum range of a series has to be an affine subspace. It has long been known that this is not the case in infinite-dimensional Banach spaces. In particular in 1984 M. I. Kadets and K. Woźniakowski obtained an example of a series whose sum range consisted of two points, and asked whether it was possible to obtain more than two, but finitely many points. This paper answers this question affirmatively, by showing how to obtain an arbitrary finite set as the sum range of a series in any infinite-dimensional Banach space.
DOI : 10.4064/sm171-3-4
Keywords: finite dimensional spaces sum range series has affine subspace has long known infinite dimensional banach spaces particular kadets niakowski obtained example series whose sum range consisted points asked whether possible obtain finitely many points paper answers question affirmatively showing obtain arbitrary finite set sum range series infinite dimensional banach space

Jakub Onufry Wojtaszczyk  1

1 Department of Mathematics, Computer Science and Mechanics University of Warsaw Banacha 2 02-097 Warszawa, Poland 
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Jakub Onufry Wojtaszczyk. A series whose sum range is an arbitrary finite set. Studia Mathematica, Tome 171 (2005) no. 3, pp. 261-281. doi: 10.4064/sm171-3-4

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