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Inequalities involving Berezin norm and Berezin number of Hilbert space operators

Journal of Mathematical Inequalities
Summary: This paper presents several Berezin number and norm inequalities for Hilbert space operators. These inequalities improve some earlier related inequalities. Among other inequalities, it is shown that if $A$ is a bounded linear operator on a Hilbert space, then \[ \mathbf{ber}^2(A) \leqslant \left\|\frac{A^\ast A + AA^\ast}{2} - \frac{1}{2R ...
Nikzat, Elham, Omidvar, Mohsen Erfanian
openaire +1 more source

Quantized Nambu-Poisson Manifolds and n-Lie Algebras

, 2010
We investigate the geometric interpretation of quantized Nambu-Poisson structures in terms of noncommutative geometries. We describe an extension of the usual axioms of quantization in which classical Nambu-Poisson structures are translated to n-Lie ...
Christian Sämann +7 more
core +1 more source

Enhancing Orange Juice Shelf Life Using Soy Lecithin‐Stabilized Lemongrass Essential Oil Nanoemulsions: Formulation, Optimization, and Application

Food Science &Nutrition, Volume 13, Issue 6, June 2025.
In this study, lemongrass essential oil (LGEO) nanoemulsions were successfully developed using soy lecithin and ultrasonication, optimizing stability and bioactivity. Grape seed oil (GSO) and Tween 80 were then integrated to enhance the nanoemulsion properties, achieving a balance between encapsulation efficiency and particle size.
Mahsa Nouraddini, Forogh Mohtarami, Mohsen Esmaiili +2 more
wiley +1 more source

On the convexity of Berezin range and Berezin radius inequalities via a class of seminorms

Bulletin des Sciences Mathématiques
This paper introduces a new family of semi-norms, say $σ_μ$-Berezin norm on the space of all bounded linear operators $B(\mathcal{H})$ defined on a reproducing kernel Hilbert space $\mathcal{H}$, namely, for each $μ\in [0,1]$ and $p\geq 1$, $$\|T\|_{σ_μ\text{-ber}}= \sup_{λ\inΩ}\left\lbrace \left(|\langle T\hat{k}_λ,\hat{k}_λ\rangle |^p~ σ_μ~ \|T\hat{k}
Athul Augustine +3 more
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An exotic calculus of Berezin–Toeplitz operators

Mathematika, Volume 71, Issue 2, April 2025.
Abstract We develop a calculus of Berezin–Toeplitz operators quantizing exotic classes of smooth functions on compact Kähler manifolds and acting on holomorphic sections of powers of positive line bundles. These functions (classical observables) are exotic in the sense that their derivatives are allowed to grow in ways controlled by local geometry and ...
Izak Oltman
wiley +1 more source

Exploring the role of beta‐endorphin in activity‐based anorexia in mice

Physiological Reports, Volume 13, Issue 3, February 2025.
Abstract Anorexia nervosa (AN) remains one of the most lethal mental health disorders and is poorly understood from a neurobiological perspective. The most widely used animal model of AN is activity‐based anorexia (ABA) where scheduled food presentation leads to a spontaneous maladaptive increase in running‐wheel activity and rapid weight loss in ...
Connor W. Christensen +3 more
wiley +1 more source

Linking Circulating Irisin and Type 2 Diabetes: A Systematic Review and Meta‐Analysis

JCSM Communications, Volume 8, Issue 1, January/June 2025.
ABSTRACT Background Type II diabetes (T2DM) is one of the most prevalent metabolic disorders, and its multisystemic health consequences are widely known. Due to skeletal muscle's ability to sequester a vast amount of glucose, muscle function and exercise have become a subject of much research into strategies to prevent and treat T2DM.
E. Aminov, P. Folan, A. Pisconti
wiley +1 more source

Central limit theorem for smooth statistics of one‐dimensional free fermions

Journal of the London Mathematical Society, Volume 111, Issue 1, January 2025.
Abstract We consider the determinantal point processes associated with the spectral projectors of a Schrödinger operator on R$\mathbb {R}$, with a smooth confining potential. In the semiclassical limit, where the number of particles tends to infinity, we obtain a Szegő‐type central limit theorem for the fluctuations of smooth linear statistics.
Alix Deleporte, Gaultier Lambert
wiley +1 more source

On the norm of the weighted Berezin transform

, 2017
We consider a weighted Berezin transform: $$ B_α : L^{\infty} (\mathbb{B}^n) \to \ \mathcal{B},\quad α>-1,$$ defined, for $f \in L^{\infty} \left( \mathbb{B}^n \right)$ and $z \in \mathbb{B}^n$, by $$(B_αf) (z) = c_α\int_{\mathbb{B}^n} \frac{\left( 1-|z|^2 \right)^{n+1}}{|1 - \langle z, w \rangle|^{2n+2}} f(w) \left( 1-|w|^2 \right)^α\ d v(w ...
openaire +2 more sources

Heart failure in Europe: Guideline‐directed medical therapy use and decision making in chronic and acute, pre‐existing and de novo, heart failure with reduced, mildly reduced, and preserved ejection fraction – the ESC EORP Heart Failure III Registry

European Journal of Heart Failure, Volume 26, Issue 12, Page 2487-2501, December 2024.
The ESC Heart Failure III Registry enrolled 10 162 patients between 2018 and 2020, with acute heart failure (HF) and in the outpatient setting, with pre‐existing and de novo HF, in cardiology and non‐cardiology settings, including patients with HF with reduced (HFrEF), mildly reduced (HFmrEF) and preserved ejection fraction (HFpEF).
Lars H. Lund +1226 more
wiley +1 more source

berezin number
reproducing kernel hilbert space
numerical range, numerical radius

inequality
fos: mathematics
functional analysis math.fa

berezin symbol
mathematics - functional analysis
berezin transform