Positive commutators of positive square-zero operators

2025/12/28 by Drnovšek, Roman, Kandić, Marko
#15B48 #46B42 #47B47 #47B65 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2512.22988

Abstract

In this paper we first consider the question which nonnegative matrices are commutators of nonnegative square-zero matrices. Then, we treat infinite-dimensional analogues of these results for operators on the Banach lattices L^p[0,1] and ℓ^p ( 1 ≤ p < ∞). In the last setting we need to extend the notion of the nonnegative rank of a nonnegative matrix.

Citations

• Positive self-commutators of positive operators
• Commutators greater than a perturbation of the identity
• Positive operators as commutators of positive operators
• On the dimension of the algebra generated by two positive semi-commuting matrices
• On the positive commutator in the radical
• On Commuting and Semi-commuting Positive Operators

Related

• Positive operators as commutators of positive operators
• Positive self-commutators of positive operators
• Sums of products of positive operators and spectra of L" uders operators
• Commutativity up to a factor for bounded and unbounded operators
• Commutators on L_p, 1≤ p<∞