Positive operators as commutators of positive operators
Abstract
It is known that a positive commutator $C=A B  B A$ 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 Pelczyński decomposition are commutators between positive operators. Our main result is also applied in the setting of a separable infinitedimensional Banach lattice $L^p(\mu)$ $(1<p<\infty)$.
 Publication:

arXiv eprints
 Pub Date:
 July 2017
 DOI:
 10.48550/arXiv.1707.00882
 arXiv:
 arXiv:1707.00882
 Bibcode:
 2017arXiv170700882D
 Keywords:

 Mathematics  Functional Analysis;
 47B07;
 47B65;
 46B42;
 47B47
 EPrint:
 20 pages