English

Once More on Positive Commutators

Functional Analysis 2013-03-21 v1 Spectral Theory

Abstract

Let A and B be bounded operators on a Banach lattice E such that the commutator C=AB-BA and the product BA are positive operators. If the product AB is a power-compact operator, then C is a quasi-nilpotent operator having a triangularizing chain of closed ideals of E. This theorem answers an open question posed in a paper by Bra\v{c}i\v{c}, Drnov\v{s}ek, Farforovskaya, Rabkin and Zem\'{a}nek.

Keywords

Cite

@article{arxiv.1211.0812,
  title  = {Once More on Positive Commutators},
  author = {Roman Drnovšek},
  journal= {arXiv preprint arXiv:1211.0812},
  year   = {2013}
}

Comments

The paper will appear in Studia Mathematica

R2 v1 2026-06-21T22:32:52.053Z