Arrangements of series preserving their convergence or boundedness

• Autorzy: Lech Drewnowski
• Języki publikacji: EN

Abstrakty

EN

For a map \(\rho\) of \(\mathbb{N}\) into itself, consider the induced transformation \(\sum_{n} x_n \mapsto \sum_{n} x_{\rho_(n)}\) of series in a topological vector space. Then such properties of this transformation as sending convergent series to convergent series, or convergent series to bounded series, or bounded series to bounded series (and a few more) are mutually equivalent. Moreover, they are equivalent to an intrinsic property of ρ which reduces to those found by Agnew and Pleasants (in the case of permutations) and Wituła (in the general case) as necessary and sufficient conditions for the above transformation to preserve convergence of scalar series. In the paper, the scalar case is treated first using simple Banach space methods, and then the result is easily extended to the general setting.

Słowa kluczowe

EN

Convergent series; bounded series; permutations of series; arrangements of series; topological vector space; spaces of bounded or convergent series

• Wydawca: Polish Mathematical Society
• Czasopismo: Commentationes Mathematicae
• Rocznik: 2007
• Tom: 47
• Numer: 1

Daty

wydano

2007

online

2017-12-19

Twórcy

autor

Lech Drewnowski

Identyfikatory

DOI

10.14708/cm.v47i1.5238