Related papers: Upper bounds for numerical radius inequalities inv…

Consider a solution $f\in C^{2}(\Omega)$ of a prescribed mean curvature equation \[ {\rm div}\left(\frac{\nabla f}{\sqrt{1+|\nabla f|^{2}}}\right)=2H(x,f) \ \ \ \ {\rm in} \ \ \Omega, \] where $\Omega\subset \Real^{2}$ is a domain whose…

For a positive integer $r$, let $f(r)$ denote the smallest number such that any 2-edge connected mixed graph with radius $r$ has an oriented radius of at most $f(r)$. Recently, Babu, Benson, and Rajendraprasad significantly improved the…

It is shown that the radial averaging operator $$ T_\omega(f)(z)=\frac{\int_{|z|}^1f\left(s\frac{z}{|z|}\right)\omega(s)\,ds}{\widehat{\omega}(z)},\quad \widehat{\omega}(z)=\int_{|z|}^1\omega(s)\,ds, $$ induced by a radial weight $\omega$…

Let $r_A(T)$ denote the $A$-spectral radius of an operator $T$ which is bounded with respect to the seminorm induced by a positive operator $A$ on a complex Hilbert space $\mathcal{H}$. In this paper, we aim to establish some $A$-spectral…

We revisit and extend known bounds on operator-valued functions of the type $$ T_1^{-z} S T_2^{-1+z}, \quad z \in \ol \Sigma = \{z\in\bbC\,|\, \Re(z) \in [0,1]\}, $$ under various hypotheses on the linear operators $S$ and $T_j$, $j=1,2$.…

We show that if $T=H+iK$ is the Cartesian decomposition of $T\in \mathbb{B(\mathscr{H})}$, then for $\alpha ,\beta \in \mathbb{R}$, $\sup_{\alpha ^{2}+\beta ^{2}=1}\Vert \alpha H+\beta K\Vert =w(T)$. We then apply it to prove that if…

Given an operator convex function $f(x)$, we obtain an operator-valued lower bound for $cf(x) + (1-c)f(y) - f(cx + (1-c)y)$, $c \in [0,1]$. The lower bound is expressed in terms of the matrix Bregman divergence. A similar inequality is…

We establish the Trudinger-Moser inequality on weighted Sobolev spaces in the whole space, and for a class of quasilinear elliptic operators in radial form of the type $\displaystyle Lu:=-r^{-\theta}(r^{\alpha}\vert…

Denote by w(A) the numerical radius of a bounded linear operator A acting on Hilbert space. Suppose that A is invertible and that the numerical radius of A and of its inverse are no greater than 1+e for some non-negative e. It is shown that…

Some new trace inequalities for operators in Hilbert spaces are provided. The superadditivity and monotonicity of some associated functionals are investigated and applications for power series of such operators are given. Some trace…

Here, we study the $q$-numerical radius of rank-one operators on a Hilbert space $\mathcal{H}$. More precisely, for $q \in [0,1]$ and $a, b \in \mathcal{H}$, we establish the formula \[ \omega_q(a \otimes b) = \frac{1}{2}\left(\|a\|\|b\| +…

Let $\mu_\alpha$ be the Lebesgue plane measure on the unit disk with the radial weight $\frac{\alpha+1}{\pi}(1-|z|^2)^\alpha$. Denote by $\mathcal{A}^{2}_{n}$ the space of the $n$-analytic functions on the unit disk, square-integrable with…

We introduce a new seminorm of $n$-tuple operators, which generalizes the $A$-Euclidean operator radius of $n$-tuple bounded linear operators on a complex Hilbert space. We introduce and study basic properties of this seminorm. As an…

Let $G=(V(G) ,E(G))$ be a digraph without loops and multiarcs, where $V(G)=\{v_1,v_2,\ldots,v_n\}$ and $E(G)$ are the vertex set and the arc set of $G$, respectively. Let $d_i^{+}$ be the outdegree of the vertex $v_i$. Let $A(G)$ be the…

In this paper, we present some extensions of the Young and Heinz inequalities for the Hilbert-Schmidt norm as well as any unitarily invariant norm. Furthermore, we give some inequalities dealing with matrices. More precisely, for two…

Let $\sigma(A)$, $\rho(A)$ and $r(A)$ denote the spectrum, spectral radius and numerical radius of a bounded linear operator $A$ on a Hilbert space $H$, respectively. We show that a linear operator $A$ satisfying $$\rho(AB)\le r(A)r(B)…

We prove several numerical radius inequalities involving positive semidefinite matrices via the Hadamard product and Kwong functions. Among other inequalities, it is shown that if $X$ is an arbitrary $n\times n$ matrix and $A,B$ are…

The problems considered in this paper come as a natural continuation of our program to develop a free analogue of Sz.-Nagy-Foias theory, for row contractions. The paper is structured as follows: Introduction Part I. Unitary invariants for…

In this paper we discuss the problem of decomposition for unbounded $2\times 2$ operator matrices by a pair of complementary invariant graph subspaces. Under mild additional assumptions, we show that such a pair of subspaces decomposes the…

Interest in higher-order tensors has recently surged in data-intensive fields, with a wide range of applications including image processing, blind source separation, community detection, and feature extraction. A common paradigm in…