4 citations · 11 across the 10 of their papers we have counts for
17 papers
On the nonnegative rank of positive operators
Roman Drnovšek, Marko Kandić
In this paper we introduce the concept of a nonnegative rank of a positive operator between ordered vector spaces. In the case of nonnegative matrices, our definit…
Positive commutators of positive square-zero operators
Roman Drnovšek, Marko Kandić
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…
On the diagonal of Riesz operators on Banach lattices
Roman Drnovšek, Marko Kandić
This paper extends the well-known Ringrose theory for compact operators to polynomially Riesz operators on Banach spaces. The particular case of an ideal-triangularizable Riesz ope…
Operator norm and numerical radius analogues of Cohen's inequality
Roman Drnovšek
Let be an invertible multiplication operator on , and let be a bounded operator on . In this note we prove that ,…
Sequences of bounds for the spectral radius of a positive operator
Roman Drnovšek
In 1992, Szyld provided a sequence of lower bounds for the spectral radius of a nonnegative matrix , based on the geometric symmetrization of powers of . In 1998, Taşçi and K…
A sharp inequality involving hyperbolic and inverse hyperbolic functions
Roman Drnovšek
We prove that the inequality holds for all . We check with the comput…
A note on Huijsmans-de Pagter problem in ordered Banach algebras
Roman Drnovšek
We give an example of a positive element in some ordered Banach algebra such that its spectrum is equal to and it is not greater than or equal to the unit element o…
On order automorphisms of the effect algebra
Roman Drnovšek
We give short proofs of two Šemrl's descriptions of order automorphisms of the effect algebra. This sheds new light on both formulas that look quite complicated. Our proofs rely on…
On algebras generated by positive operators
Roman Drnovšek
We study algebras generated by positive matrices, i.e., matrices with nonnegative entries. Some of our results hold in more general setting of vector lattices. We reprove and exten…
Positive operators as commutators of positive operators
Roman Drnovšek, Marko Kandić
It is known that a positive commutator between positive operators on a Banach lattice is quasinilpotent whenever at least one of and is compact. In this paper…
When powers of a matrix coincide with its Hadamard powers
Roman Drnovšek
We characterize matrices whose powers coincide with their Hadamard powers.
Triangularizability of trace-class operators with increasing spectrum
Roman Drnovšek
For any measurable set of a measure space , let be the (orthogonal) projection on the Hilbert space with the range $ran \, P_E = \{f \in L^2(X, μ) : f…
The spread of the spectrum of a nonnegative matrix with a zero diagonal element
Roman Drnovšek
Let be a nonnegative matrix with . We prove some lower bounds for the spread of that is defined as the maximum distance between an…
On the S-matrix conjecture
Roman Drnovšek
Motivated with a problem in spectroscopy, Sloane and Harwit conjectured in 1976 what is the minimal Frobenius norm of the inverse of a matrix having all entries from the interval […
Once More on Positive Commutators
Roman Drnovšek
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, th…
The von Neumann entropy and unitary equivalence of quantum states
Roman Drnovšek
K. He, J. Hou, and M. Li have recently given a sufficient and necessary condition for unitary equivalence of quantum states. This condition is based on the von Neumann entropy. In…
On semigroups of matrices with nonnegative diagonals
Grega Cigler, Roman Drnovšek
We give a short proof of a recent result by Bernik, Mastnak, and Radjavi, stating that an irreducible group of complex matrices with nonnegative diagonal entries is diagonally simi…