Related papers: Some trace inequalities for exponential and logari…

We give systematic ways of defining monotone quantum relative entropies and (multi-variate) quantum R\'enyi divergences starting from a set of monotone quantum relative entropies. Despite its central importance in information theory, only…

Applying Zvonkin's transform, the exponential convergence in Wasserstein distance for a class of functional SDEs with H\"older continuous drift is obtained. This combining with log-Harnack inequality implies the same convergence in the…

We consider a new functional inequality controlling the rate of relative entropy decay for random walks, the interchange process and more general block-type dynamics for permutations. The inequality lies between the classical logarithmic…

In this article, we prove that convex functions and log-convex functions obey certain general refinements that lead to several refinements and reverses of well known inequalities for matrices, including Young's inequality, Heinz inequality,…

Let y1, y2, y3, a1, a2, a3 > 0 be such that y1 y2 y3 = a1 a2 a3 and y1 + y2 + y3 >= a1 + a2 + a3, y1 y2 + y2 y3 + y1 y3 >= a1 a2 + a2 a3 + a1 a3. Then the following inequality holds (log y1)^2 + (log y2)^2 + (log y3)^2 >= (log a1)^2 + (log…

We obtain several versions of the Hausdorff-Young and Hardy-Littlewood inequalities for the $(k,a)$-generalized Fourier transform recently investigated at length by Ben Sa\"i d, Kobayashi, and {\O} rsted. We also obtain a number of weighted…

We show that under minimal assumptions on a class of functions $\mathcal{H}$ defined on a probability space $(\mathcal{X},\mu)$, there is a threshold $\Delta_0$ satisfying the following: for every $\Delta\geq\Delta_0$, with probability at…

Let $1\leq p <\infty$ and $0 < q,r < \infty$. We characterize validity of the inequality for the composition of the Hardy operator, \begin{equation*} \bigg(\int_a^b \bigg(\int_a^x \bigg(\int_a^t f(s)ds \bigg)^q u(t) dt \bigg)^{\frac{r}{q}}…

We prove that the quantum relative entropy decreases monotonically under the application of any positive trace-preserving linear map, for underlying separable Hilbert spaces. This answers in the affirmative a natural question that has been…

In this paper, we generalize several Berezin number inequalities involving product of operators. For instance, we show that if $A, B$ are positive operators and $X$ is any operator, then \begin{align*}…

Entropy-like functionals on operator algebras have been studied since the pioneering work of von Neumann, Umegaki, Lindblad, and Lieb. The most well-known are the von Neumann entropy $trace (\rho\log \rho)$ and a generalization of the…

Eigenvalues inequalities involving (log) convex/concav functions and Hermitian matrices, positive unital maps are considered. Simple proofs of Bhatia-Kittaneh inequality and Naimark dilation theorem are given.

Quantum generalizations of Renyi's entropies are a useful tool to describe a variety of operational tasks in quantum information processing. Two families of such generalizations turn out to be particularly useful: the Petz quantum Renyi…

In this note, we briefly introduce the background and motivation of the collaborative work [arXiv:2508.20797], and provide an outline of the main results. The latter relates to matrix and higher order scalar differential equations satisfied…

We establish two inequalities in real inner product spaces. The first is a multiplicative strengthening of the classical Hornich-Hlawka inequality: for all vectors $x, y, z$ in a real inner product space $H$ \[ \|x\|\,\|y\| +…

Quantum f-divergences are a quantum generalization of the classical notion of f-divergences, and are a special case of Petz' quasi-entropies. Many well known distinguishability measures of quantum states are given by, or derived from,…

We study properties of ridge functions $f(x)=g(a\cdot x)$ in high dimensions $d$ from the viewpoint of approximation theory. The considered function classes consist of ridge functions such that the profile $g$ is a member of a univariate…

In this article, we introduce an infinite-dimensional analogue of the $\alpha$-stable L\'evy motion, defined as a L\'evy process $Z=\{Z(t)\}_{t \geq 0}$ with values in the space $\mathbb{D}$ of c\`adl\`ag functions on $[0,1]$, equipped with…

Let $\alpha_1,\alpha_2$ be non-zero algebraic numbers such that $\frac{\log \alpha_2}{\log\alpha_1}\notin\mathbb{Q}$ and let $\beta$ be a quadratic irrational number. In this article, we prove that the values of two relatively prime…

We prove a trace Hardy type inequality with the best constant on the polyhedral convex cones which generalizes recent results of Alvino et al. and of Tzirakis on the upper half space. We also prove some trace Hardy-Sobolev-Maz'ya type…