- Tytuł:
- Balancing vectors and convex bodies
- Autorzy:
- Banaszczyk, Wojciech
- Powiązania:
- https://bibliotekanauki.pl/articles/1292627.pdf
- Data publikacji:
- 1993
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
balancing vectors
Steinitz constant - Opis:
- Let U, V be two symmetric convex bodies in $ℝ^n$ and |U|, |V| their n-dimensional volumes. It is proved that there exist vectors $u_1,...,u_n ∈ U$ such that, for each choice of signs $ε_1,...,ε_n = ± 1$, one has $ε_1 u_1 + ... + ε_n u_n ∉ rV$ where $r = (2πe^2)^{-1/2} n^{1/2}(|U|/|V|)^{1/n}$. Hence it is deduced that if a metrizable locally convex space is not nuclear, then it contains a null sequence $(u_n)$ such that the series $∑_{n = 1}^∞ ε_n u_{π(n)}$ is divergent for any choice of signs $ε_n = ± 1$ and any permutation π of indices.
- Źródło:
-
Studia Mathematica; 1993, 106, 1; 93-100
0039-3223 - Pojawia się w:
- Studia Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł