An example concerning bounded linear regularity of subspaces in Hilbert space

Authors

  • S. Reich
  • A. J. Zaslavski

Keywords:

Bounded regularity, Hilbert space, subspace

Abstract

We study bounded linear regularity of finite sets of closed subspaces in a Hilbert space. In particular, we construct for each natural number \(n \ge 3\), a set of \(n\) closed subspaces of \(\ell^{2}\) which has the bounded linear regularity property, while the bounded linear regularity property does not hold for each one of its nonempty, proper non-singleton subsets. We also establish a related theorem regarding the bounded regularity property in metric spaces. 10.1017/S0004972713000749

Published

2014-01-27

Issue

Vol. 89 No. 2 (2014)

Section

Articles
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