Geodesic
Spectral radius inequalities for positive commutators
Czechoslovak Mathematical Journal, Tome 64 (2014) no. 1, pp. 1-10
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We establish several inequalities for the spectral radius of a positive commutator of positive operators in a Banach space ordered by a normal and generating cone. The main purpose of this paper is to show that in order to prove the quasi-nilpotency of the commutator we do not have to impose any compactness condition on the operators under consideration. In this way we give a partial answer to the open problem posed in the paper by J. Bračič, R. Drnovšek, Y. B. Farforovskaya, E. L. Rabkin, J. Zemánek (2010). Inequalities involving an arbitrary commutator and a generalized commutator are also discussed.
We establish several inequalities for the spectral radius of a positive commutator of positive operators in a Banach space ordered by a normal and generating cone. The main purpose of this paper is to show that in order to prove the quasi-nilpotency of the commutator we do not have to impose any compactness condition on the operators under consideration. In this way we give a partial answer to the open problem posed in the paper by J. Bračič, R. Drnovšek, Y. B. Farforovskaya, E. L. Rabkin, J. Zemánek (2010). Inequalities involving an arbitrary commutator and a generalized commutator are also discussed.
DOI : 10.1007/s10587-014-0077-x
Classification : 47A10, 47B47, 47B65
Keywords: cone; positive operator; commutator; spectral radius 
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Zima, Mirosława. Spectral radius inequalities for positive commutators. Czechoslovak Mathematical Journal, Tome 64 (2014) no. 1, pp. 1-10. doi: 10.1007/s10587-014-0077-x

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