Positive operators as commutators of positive operators

DOI10.4064/SM170703-26-9zbMATH Open1505.47039arXiv1707.00882OpenAlexW2964143708WikidataQ129502276 ScholiaQ129502276MaRDI QIDQ4963339

Marko Kandić, Roman Drnovšek

Publication date: 1 November 2018

Published in: Studia Mathematica (Search for Journal in Brave)

Abstract: It is known that a positive commutator $C=AB-BA$ between positive operators on a Banach lattice is quasinilpotent whenever at least one of $A$ and $B$ is compact. In this paper we study the question under which conditions a positive operator can be written as a commutator between positive operators. As a special case of our main result we obtain that positive compact operators on order continuous Banach lattices which admit order Pelczy'nski decomposition are commutators between positive operators. Our main result is also applied in the setting of a separable infinite-dimensional Banach lattice $L^p(mu)$ $(1<p<infty)$.

Full work available at URL: https://arxiv.org/abs/1707.00882

zbMATH Keywords

compact operatorsnilpotent operatorspositive commutatorsorder Pełczyński decomposition

Mathematics Subject Classification ID

Banach lattices (46B42) Linear operators defined by compactness properties (47B07) Commutators, derivations, elementary operators, etc. (47B47) Positive linear operators and order-bounded operators (47B65)

Cites Work

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