Weak cluster points of a sequence and coverings by cylinders
| dc.creator | Kadets, Vladimir | |
| dc.date | 2003-12-05 | |
| dc.date.accessioned | 2026-07-07T05:03:37Z | |
| dc.date.available | 2026-07-07T05:03:37Z | |
| dc.description | Let $H$ be a Hilbert space. Using Ball's solution of the "complex plank problem" we prove that the following properties of a sequence $a_n>0$ are equivalent: (1) There is a sequence $x_n \in H$ with $\|x_n\|=a_n$, having 0 as a weak cluster point; (2) $\sum_1^\infty a_n^{-2}=\infty$. Using this result we show that a natural idea of generalization of Ball's "complex plank" result to cylinders with $k$-dimensional base fails already for $k=3$. We discuss also generalizations of "weak cluster points" result to other Banach spaces and relations with cotype. | |
| dc.description | 6 pages | |
| dc.identifier | https://arxiv.org/abs/math/0312131 | |
| dc.identifier | http://arxiv.org/abs/math/0312131 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69490 | |
| dc.subject | Functional Analysis | |
| dc.subject | 46C05; 46B20 | |
| dc.title | Weak cluster points of a sequence and coverings by cylinders | |
| dc.type | text |