A series whose sum range is an arbitrary finite set

• Autorzy: Jakub Onufry Wojtaszczyk
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 40A30: Convergence and divergence of series and sequences of functions
• 46B15: Summability and bases

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2005
• Tom: 171
• Numer: 3
• Strony: 261-281

Daty

wydano

2005

Twórcy

autor

Jakub Onufry Wojtaszczyk

• Department of Mathematics, Computer Science and Mechanics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland

Identyfikatory

DOI

10.4064/sm171-3-4