1. Freedom in constructing quasi-copulas vs. copulasMatjaž Omladič, Nik Stopar, 2025, izvirni znanstveni članek Povzetek: The main goal of this paper is to study the extent of freedom one has in constructing quasi-copulas vs. copulas. Specifically, it exhibits three construction methods for quasi-copulas based on recent developments: a representation of multivariate quasi-copulas by means of infima and suprema of copulas, an extension of a classical result on shuffles of min to the setting of quasi-copulas, and a construction method for quasi-copulas obeying a given signed mass pattern on a patch.
Ključne besede: copulas, quasi-copulas, shuffles of min, patch, lattices
Objavljeno v DiRROS: 09.04.2025; Ogledov: 123; Prenosov: 51
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2. On the diagonal of Riesz operators on Banach latticesRoman Drnovšek, Marko Kandić, 2024, izvirni znanstveni članek Povzetek: 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 operator on an order continuous Banach lattice yields that the spectrum of such operator lies on its diagonal, which motivates the systematic study of an abstract diagonal of a regular operator on an order complete vector lattice $E$. We prove that the class $\mathscr D$ of regular operators for which the diagonal coincides with the atomic diagonal is always a band in $\mathcal L_r(E)$, which contains the band of abstract integral operators. If $E$ is also a Banach lattice, then $\mathscr D$ contains positive Riesz and positive AM-compact operators.
Ključne besede: vector lattices, Banach lattices, Riesz operators, diagonal of an operator
Objavljeno v DiRROS: 24.01.2025; Ogledov: 208; Prenosov: 104
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3. Commutators greater than a perturbation of the identityRoman Drnovšek, Marko Kandić, 2025, izvirni znanstveni članek Povzetek: Let $a$ and $b$ be elements of an ordered normed algebra ${\mathcal A}$ with unit $e$. Suppose that the element $a$ is positive and that for some $\varepsilon > 0$ there exists an element $x\in {\mathcal A}$ with $\|x\|\leq \varepsilon$ such that $ab-ba \geq e+x$. If the norm on ${\mathcal A}$ is monotone, then we show $\|a\|\cdot \|b\|\geq \tfrac{1}{2} \ln \tfrac{1}{\varepsilon}$, which can be viewed as an order analog of Popa's quantitative result for commutators of operators on Hilbert spaces. We also give a relevant example of positive operators $A$ and $B$ on the Hilbert lattice $\ell^2$ such that their commutator $A B - B A$ is greater than an arbitrarily small perturbation of the identity operator.
Ključne besede: Banach lattices, positive operators, commutators, ordered normed algebras
Objavljeno v DiRROS: 19.09.2024; Ogledov: 320; Prenosov: 193
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