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AN EXAMPLE CONCERNING BOUNDED LINEAR REGULARITY OF SUBSPACES IN HILBERT SPACE

Part of: Normed linear spaces and Banach spaces; Banach lattices

Published online by Cambridge University Press:  12 September 2013

SIMEON REICH  and
ALEXANDER J. ZASLAVSKI
SIMEON REICH*
Affiliation:
Department of Mathematics, The Technion – Israel Institute of Technology, 32000 Haifa, Israel email ajzasl@tx.technion.ac.il
ALEXANDER J. ZASLAVSKI
Affiliation:
Department of Mathematics, The Technion – Israel Institute of Technology, 32000 Haifa, Israel email ajzasl@tx.technion.ac.il
*
✉sreich@tx.technion.ac.il
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Abstract

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We study bounded linear regularity of finite sets of closed subspaces in a Hilbert space. In particular, we construct for each natural number $n\geq 3$ 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 nonsingleton subsets. We also establish a related theorem regarding the bounded regularity property in metric spaces.

Keywords

bounded regularityHilbert spacesubspace

MSC classification

Secondary: 46C05: Hilbert and pre-Hilbert spaces
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 89 , Issue 2 , April 2014 , pp. 217 - 226
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc. 

References

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