Related papers: On an operator Kantorovich inequality for positive…

Kato's inequality is shown for the magnetic relativistic Schr\"odinger operator $H_{A,m}$ defined as the operator theoretical {\it square root} of the selfadjoint, magnetic nonrelativistic Schr\"odinger operator $(-i\nabla-A(x))^2+m^2$ with…

We extend to the multilinear setting classical inequalities of Marcinkiewicz and Zygmund on $\ell^r$-valued extensions of linear operators. We show that for certain $1 \leq p, q_1, \dots, q_m, r \leq \infty$, there is a constant $C\geq 0$…

We give new inequalities for $A$-operator seminorm and $A$-numerical radius of semi-Hilbertian space operators and show that the inequalities obtained here generalize and improve on the existing ones. Considering a complex Hilbert space…

Given a C$^*$-algebra $A$, let $S(A^+)$ denote the set of those positive elements in the unit sphere of $A$. Let $H_1$, $H_2,$ $H_3$ and $H_4$ be complex Hilbert spaces, where $H_3$ and $H_4$ are infinite-dimensional and separable. In this…

Several refinements of norm and numerical radius inequalities of bounded linear operators on a complex Hilbert space are given. In particular, we show that if $A$ is a bounded linear operator on a complex Hilbert space, then $$…

The main object of this paper is to improve some of the known estimates for classical Kantorovich operators. A quantitative Voronovskaya-type result in terms of second moduli of continuity which improves some previous results is obtained.…

In this paper we consider a version of the Kantorovich's theorem for solving the generalized equation $F(x)+T(x)\ni 0$, where $F$ is a Fr\'echet derivative function and $T$ is a set-valued and maximal monotone acting between Hilbert spaces.…

On finite dimensional spaces, it is apparent that an operator is the product of two positive operators if and only if it is similar to a positive operator. Here, the class ${\mathcal L}^{+2}$ of bounded operators on separable infinite…

Let $\mathcal{H}$ be a right quaternionic Hilbert space and let $T$ be a quaternionic normal operator with the domain $\mathcal{D}(T) \subset \mathcal{H}$. Then for a fixed unit imaginary quaternion $m$, there exists a Hilbert basis…

We establish a general operator parallelogram law concerning a characterization of inner product spaces, get an operator extension of Bohr's inequality and present several norm inequalities. More precisely, let ${\mathfrak A}$ be a…

We will show that for any two bounded linear operators $X,Y$ on a Hilbert space ${\frak H}$, if they satisfy the triangle equality $|X+Y|=|X|+|Y|$, there exists a partial isometry $U$ on ${\frak H}$ such that $X=U|X|$ and $Y=U|Y|$. This is…

A bounded linear operator $A$ on a Hilbert space is posinormal if there exists a positive operator $P$ such that $AA^{*} = A^{*}PA$. Posinormality of $A$ is equivalent to the inclusion of the range of $A$ in the range of its adjoint $A^*$.…

We present a logarithmic Sobolev inequality adapted to a log-concave measure. Assume that $\Phi$ is a symmetric convex function on $\dR$ satisfying $(1+\e)\Phi(x)\leq {x}\Phi'(x)\leq(2-\e)\Phi(x)$ for $x\geq0$ large enough and with…

In this paper, we present some operator and eigenvalue inequalities involving operator monotone, doubly concave and doubly convex functions. These inequalities provide some variants of operator Acz\'{e}l inequality and its reverse via…

Researchers have identified complex matrices $A$ such that a bounded linear operator $B$ acting on a Hilbert space will admit a dilation of the form $A \otimes I$ whenever the numerical range inclusion relation $W(B) \subseteq W(A)$ holds.…

Consider a positive operator $T$ on an $L^p$-space (or, more generally, a Banach lattice) which increases the support of functions in the sense that $supp(Tf) \supseteq supp{f}$ for every function $f \ge 0$. We show that this implies, under…

In this work, generalization of some inequalities for continuous $h$-synchronous ($h$-asynchronous) functions of selfadjoint linear operators in Hilbert spaces are proved.

We present a lower error bound for approximating linear multivariate operators defined over Hilbert spaces in terms of the error bounds for appropriately constructed linear functionals as long as algorithms use function values. Furthermore,…

Employing the notion of operator log-convexity, we study joint concavity$/$ convexity of multivariable operator functions: $(A,B)\mapsto F(A,B)=h\left[ \Phi(f(A))\ \sigma\ \Psi(g(B))\right]$, where $\Phi$ and $\Psi$ are positive linear maps…

In this paper, we present generalized P\'olya-Szeg\"o type inequalities for positive invertible operators on a Hilbert space for arbitrary operator means between the arithmetic and the harmonic means. As applications, we present Operator…