Spectral radius inequalities for positive commutators

Mirosława Zima

Czechoslovak Mathematical Journal (2014)

  • Volume: 64, Issue: 1, page 1-10
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Zima, Mirosława. "Spectral radius inequalities for positive commutators." Czechoslovak Mathematical Journal 64.1 (2014): 1-10. <http://eudml.org/doc/262054>.

@article{Zima2014,
abstract = {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.},
author = {Zima, Mirosława},
journal = {Czechoslovak Mathematical Journal},
keywords = {cone; positive operator; commutator; spectral radius; cone; positive operator; commutator; spectral radius},
language = {eng},
number = {1},
pages = {1-10},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Spectral radius inequalities for positive commutators},
url = {http://eudml.org/doc/262054},
volume = {64},
year = {2014},
}

TY - JOUR
AU - Zima, Mirosława
TI - Spectral radius inequalities for positive commutators
JO - Czechoslovak Mathematical Journal
PY - 2014
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 64
IS - 1
SP - 1
EP - 10
AB - 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.
LA - eng
KW - cone; positive operator; commutator; spectral radius; cone; positive operator; commutator; spectral radius
UR - http://eudml.org/doc/262054
ER -

References

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