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Sums of products of positive operators and spectra of Lüders operators


Author: Bojan Magajna
Journal: Proc. Amer. Math. Soc. 141 (2013), 1349-1360
MSC (2010): Primary 47A05, 47B47; Secondary 47N50, 81P45
DOI: https://doi.org/10.1090/S0002-9939-2012-11537-0
Published electronically: September 4, 2012
MathSciNet review: 3008882
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Abstract: Each bounded operator $ T$ on an infinite dimensional Hilbert space $ \mathcal {H}$ is a sum of three operators that are similar to positive operators; two such operators are sufficient if $ T$ is not a compact perturbation of a scalar. The spectra of Lüders operators (elementary operators on $ \mathrm {B}(\mathcal {H})$ with positive coefficients) of lengths at least three are not necessarily contained in $ \mathrm {B}(\mathcal {H})^+$. On the other hand, the spectra of such operators of lengths (at most) two are contained in $ \mathrm {B}(\mathcal {H})^+$ if the coefficients on one side commute.


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Additional Information

Bojan Magajna
Affiliation: Department of Mathematics, University of Ljubljana, Jadranska 21, Ljubljana 1000, Slovenia
Email: Bojan.Magajna@fmf.uni-lj.si

DOI: https://doi.org/10.1090/S0002-9939-2012-11537-0
Keywords: Positive operators, commutators, quantum operations
Received by editor(s): August 19, 2011
Published electronically: September 4, 2012
Communicated by: Richard Rochberg
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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