Related papers: A glimpse at the operator Kantorovich inequality

I will show that operator of analytic (harmonic) continuation on a lattice graph has a positive spectrum. I use a theorem about positivity of eigenvalues of totally positive matrices. I conjecture that by approximation the similar result…

We establish the weighted fractional Orlicz-Hardy inequalities for various Orlicz functions. Further, we identify the critical cases for each Orlicz function and prove the weighted fractional Orlicz-Hardy inequalities with logarithmic…

Let $\mathcal{H}$ be a Hilbert space, and let $K(\mathcal{H})$ be the $C^*$-algebra of compact operators on $\mathcal{H}$. In this paper, we present some characterizations of the norm-parallelism for elements of a Hilbert…

In this paper we study operators of the form $M(\phi)=T(\phi)+H(\phi)$ where $T(\phi)$ and $H(\phi)$ are the Toeplitz and Hankel operators acting on $H^p(\T)$ with generating function $\phi\in L^\iy(\T)$. It turns out that $M(\phi)$ is…

This paper investigates composition operators and weighted composition operators on semi-Hilbert spaces induced by positive multiplication operators on \( L^2(\mu) \). Within the framework of \( A \)-adjoint operators, we characterize…

In this paper, we introduce the concept of operator arithmetic-geometrically convex functions for positive linear operators and prove some Hermite-Hadamard type inequalities for these functions. As applications, we obtain trace inequalities…

Mond and Pecaric proposed a powerful method, namd as MP method, to deal with operator inequalities. However, this method requires a real-valued function to be convex or concave, and the normalized positive linear map between Hilbert spaces.…

We study the spectrum of the differential operator T generated by the differential expression of order n>2 with the m by m PT-symmetric periodic matrix coefficients. The case when m and n are the odd numbers was investigated in [8]. In this…

Given a homogeneous k-th order differential operator $A (D)$ on $\mathbb{R}^n$ between two finite dimensional spaces, we establish the Hardy inequality $$\int_{\mathbb{R}^n} \frac{\lvert D^{k-1}u\rvert}{\lvert x \rvert} \,\mathrm{d} x \leq…

Given a complex, separable Hilbert space $\mathcal{H}$, we characterize those operators for which $\| P T (I-P) \| = \| (I-P) T P \|$ for all orthogonal projections $P$ on $\mathcal{H}$. When $\mathcal{H}$ is finite-dimensional, we also…

Let $H$ be the Hardy operator and $I$ the identity operator acting on functions on the real half-line. We find optimal bounds for the operator $H - I$ in the setting of power weights and the cases of positive decreasing functions, positive…

Let $H$ be a complex separable Hilbert space and $B(H)$ the algebra of all bounded linear operators on $H$. In this paper, we give considerable generalizations of the inequalities for norms of commutators of normal operators. Let $S, T \in…

A linear map $\Phi$ between matrix spaces is called cross-positive if it is positive on orthogonal pairs $(U,V)$ of positive semidefinite matrices in the sense that $\langle U,V\rangle:=\text{Tr}(UV)=0$ implies $\langle…

We present an extension of the Hardy--Littlewood inequality for multilinear forms. More precisely, let $\mathbb{K}$ be the real or complex scalar field and $m,k$ be positive integers with $m\geq k\,$ and $n_{1},\dots ,n_{k}$ be positive…

We present a Diaz--Metcalf type operator inequality as a reverse Cauchy-Schwarz inequality and then apply it to get the operator versions of P\'{o}lya-Szeg\"{o}'s, Greub-Rheinboldt's, Kantorovich's, Shisha-Mond's, Schweitzer's, Cassels' and…

In this research article the necessary and sufficient conditions for the norm of composition operator $C_{\Phi}$ on $\mathcal{A}_{\alpha}^2(H)$ to be one are obtained. Moreover, $C_{\Phi}$ is unitary on $\mathcal{A}_{\alpha}^2(H)$ if and…

Let $m \geq 1$ be an integer and let $H_m(\mathbb B)$ be the analytic functional Hilbert space on the unit ball $\mathbb B \subset \mathbb C^n$ given by the reproducing kernel $K_m(z,w) = (1 - \langle z,w \rangle)^{-m}$. We prove that…

In this article, we proved upper bounds for numerical radius of bounded linear operator and product of operators which generalize and improve existing inequalities. We also obtain a numerical radius inequality of invertible operator using…

In this contribution we solve the following problem. Let H_{nm} be a Hilbert space of dimension nm, and let A be a positive semidefinite self-adjoint linear operator on H_{nm}. Under which conditions on the spectrum has A a positive partial…

Let $\mathcal{H}$ be the class of harmonic functions $f=h+\overline{g}$ in the unit disk $\mathbb{D}:=\{z\in\mathbb{C}:|z|<1\}$, where $h$ and $g$ are analytic in $\mathbb{D}$ with the normalization $h(0)=g(0)=h'(0)-1=0$. Let…