This is an announcement for the paper "A series whose sum range is an arbitrary finite set" by Jakub Onufry Wojtaszczyk.
Abstract: In 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. Wo`{z}niakowski 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.
Archive classification: math.FA
Mathematics Subject Classification: 46B15
Citation: Studia Mathematica 171 (3) (2005), pp. 261-281
Remarks: 21 pages
The source file(s), npunktow.tex: 64310 bytes, is(are) stored in gzipped form as 0803.0415.gz with size 20kb. The corresponding postcript file has gzipped size 127kb.
Submitted from: onufryw@gmail.com
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