Weak Cluster Points of a Sequence and Coverings by Cylinders

@inproceedings{KADETS2004WeakCP,
title={Weak Cluster Points of a Sequence and Coverings by Cylinders},
author={VLADIMIR KADETS},
year={2004}
}

VLADIMIR KADETS

Published 2004

Let H be a Hilbert space. Using Ball’s solution of the ”complex plank problem” we prove that the following properties of a sequence an > 0 are equivalent: (1) There is a sequence xn ∈ H with ‖xn‖ = an, having 0 as a weak cluster point; (2) ∑ ∞ 1 a −2 n = ∞. 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… CONTINUE READING