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Operators in finite distributive subspace lattices, I

Published online by Cambridge University Press:  24 October 2008

N. K. Spanoudakis
N. K. Spanoudakis
Affiliation:
Department of Mathematics, University of Crete, 714 09Iraklio, Crete, Greece
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Abstract

The purpose of this paper is to settle in the negative an open problem in operator theory, which asks whether in a finite distributive subspace lattice ℒ on a Hilbert space, every finite rank operator of Alg ℒ can be written as a finite sum of rank one operators from Alg ℒ. The counter-example constructed is on a specific Hilbert space realization of the free distributive lattice on three generators and the operator which fails the above property has rank two.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 113 , Issue 1 , January 1993 , pp. 141 - 146
Copyright
Copyright © Cambridge Philosophical Society 1993

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References

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