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

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Convex Geometry and Functional Analysis, in W.B.Johnson and J.Lindenstrauss (editors) Handbook of the geometry of Banach spaces, vol

  • Keith Ball
  • 2001

The complex plank

  • Keith Ball
  • problem, Bull. London Math. Soc
  • 2001
1 Excerpt

A solution of the ”Plank problem

  • T. Bang
  • Proc. Amer. Math. Soc
  • 1951
1 Excerpt

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