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EntropyDue to the classifying theorems by Petz and Kubo–Ando, we know that there are bijective correspondences between Quantum Fisher Information(s), operator means, and the class of symmetric, normalized operator monotone functions on the positive half line ...
Paolo Gibilisco
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Some inequalities for operator monotone functions
Annals of the West University of Timisoara: Mathematics and Computer Science, 2022 In this paper we show that, if that the function f : [0, ∞) → 𝔾 is operator monotone in [0, ∞) then there exist b ≥ 0 and a positive measure m on [0, ∞) such that [f(B)-f(A)](B-A)==b(B-A)2+∫0∞s2[∫01[((1-t)A+tB+s)-1(B-A)]2dt]dm(s)\matrix{ {\left[ {f ...
Dragomir Silvestru Sever
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Around Operator Monotone Functions [PDF]
Integral Equations and Operator Theory, 2011 We show that the symmetrized product $AB+BA$ of two positive operators $A$ and $B$ is positive if and only if $f(A+B)\leq f(A)+f(B)$ for all non-negative operator monotone functions $f$ on $[0,\infty)$ and deduce an operator inequality. We also give a necessary and sufficient condition for that the composition $f\circ g$ of an operator convex function $
Moslehian, Mohammad Sal, Najafi, Hamed
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Application of operator monotone functions in economics; pp. 42–47 [PDF]
Proceedings of the Estonian Academy of Sciences, 2010 Operator monotone functions play an important role in economics. We show that 2-monotonicity is equivalent to decreasing relative risk premium, a notion recently introduced in microeconomics.
Frank Hansen
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Cubo, 2023 For a continuous and positive function $w\left( \lambda \right) ,$ $\lambda >0$ and $\mu $ a positive measure on $(0,\infty )$ we consider the following integral transform % \begin{equation*} \mathcal{D}\left( w,\mu \right) \left( T\right) :=\int_{0}^{
S. S. Dragomir
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New Integral Inequalities Relating to a General Integral Operators Through Monotone Functions [PDF]
Sahand Communications in Mathematical Analysis, 2022 Weighted integral inequalities for general integral operators on monotone positive functions with parameters $p$ and $q$ are established in [4]. The aim of this work is to extend the results to different cases of these parameters, in particular for ...
Bouharket Benaissa, Abdelkader Senouci
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Gradient Inequalities for an Integral Transform of Positive Operators in Hilbert Spaces
Annales Mathematicae Silesianae, 2023 For a continuous and positive function w (λ) , λ > 0 and µ a positive measure on (0, ∞) we consider the following integral transform 𝒟(w,μ)(T):=∫0∞w(λ)(λ+T)-1dμ(λ),\mathcal{D}\left( {w,\mu } \right)\left( T \right): = \int_0^\infty {w\left( \lambda ...
Dragomir Silvestru Sever
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Long-term behavior of nonautonomous neutral compartmental systems
Electronic Journal of Qualitative Theory of Differential Equations, 2022 The asymptotic behavior of the trajectories of compartmental systems with a general set of admissible initial data is studied. More precisely, these systems are described by families of monotone nonautonomous neutral functional differential equations ...
Sylvia Novo, Víctor Villarragut
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Some operator monotone functions [PDF]
Proceedings of the American Mathematical Society, 1972 A short proof is given based on C*-algebra theory for the well-known theorem that if S and Tare bounded selfadjoint operators on a Hubert space such that 0^5^T then Sai|7"a for each0^a 0; and S+e/and T+el are both invertible. Since (S+eI)x converges to Sx in norm when e-0 for each a>0, and since the positive operators in B(%>) form a norm closed set ...
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Functional voting operators: the non-monotonic case [PDF]
Mathematical Social Sciences, 1993 This paper was written during the first author's visit to the Division of the Humanities and Social Sciences at the California Institute of Technology. Partial financial support was received from the Caltech Laboratory for Experimental Economics and Political Science. Published as Aleskerov, Fuad, and John Duggan.
Aleskerov, Fuad, Duggan, John
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