Operators in finite distributive subspace lattices, I

Operators in finite distributive subspace lattices, I

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 const...

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Veröffentlicht in:Mathematical proceedings of the Cambridge Philosophical Society 1993-01, Vol.113 (1), p.141-146
1. Verfasser: Spanoudakis, N. K.
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Exact sciences and technology
Mathematical analysis
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Sciences and techniques of general use
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container_title Mathematical proceedings of the Cambridge Philosophical Society
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description 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.
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subjects Exact sciences and technology
Mathematical analysis
Mathematics
Operator theory
Sciences and techniques of general use
title Operators in finite distributive subspace lattices, I
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