Related papers: Two-sided multiplication operators on the space of…

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*}…

Let $L$ be a linear operator in $L^2({{\mathbb R}^n})$ and generate an analytic semigroup $\{e^{-tL}\}_{t\ge 0}$ with kernels satisfying an upper bound of Poisson type, whose decay is measured by $\theta(L)\in (0,\infty].$ Let $\omega$ on…

We prove that every bounded linear operator between Lipschitz spaces admits a lifting along the De Leeuw embedding. More precisely, given pointed metric spaces $M$ and $N$ and $\epsilon>0$, every bounded linear operator…

We develop upper and lower bounds for the numerical radius of $2\times 2$ off-diagonal operator matrices, which generalize and improve on the existing ones. We also show that if $A$ is a bounded linear operator on a complex Hilbert space…

Let $T:Y\to X$ be a bounded linear operator between two normed spaces. We characterize compactness of $T$ in terms of differentiability of the Lipschitz functions defined on $X$ with values in another normed space $Z$. Furthermore, using a…

We study multiplication operators on the weighted Banach spaces of an infinite tree. We characterize the bounded and the compact operators, as well as determine the operator norm. In addition, we determine the spectrum of the bounded…

We present a sufficient condition for smoothness of bounded linear operators on Banach spaces for the first time. Let $T, A \in B(\mathbb{X}, \mathbb{Y}),$ where $\mathbb{X}$ is a real Banach space and $\mathbb{Y}$ is a real normed linear…

We prove that every multiplier M (bounded operator commuting with the shift operator) on a large class of Banach spaces of sequences on Z is associated to a function essentially bounded by the norm of M on the spectrum of S.

Let $(M, {g})$ be a compact, $d$-dimensional Riemannian manifold without boundary. Suppose further that $(M,g)$ is either two dimensional and has no conjugate points or $(M,g)$ has non-positive sectional curvature. The goal of this note is…

We obtain a general Marcinkiewicz-type multiplier theorem for mixed systems of strongly commuting operators $L=(L_1,...,L_d);$ where some of the operators in $L$ have only a holomorphic functional calculus, while others have additionally a…

Let $\mathcal{L}$ be the space of complex-valued functions $f$ on the set of vertices $T$ of an rooted infinite tree rooted at $o$ such that the difference of the values of $f$ at neighboring vertices remains bounded throughout the tree,…

The aim of this article is to extend results of M.~Popov and second named author about orthogonally additive narrow operators on vector lattices. The main object of our investigations are an orthogonally additive narrow operators between…

Let $A\in\mathcal{B}(X)$, $B\in\mathcal{B}(Y)$ and $C\in\mathcal{B}(Y,X)$ where $X$ and $Y$ are infinite Banach or Hilbert spaces. Let $M_{C}=\begin{pmatrix} A & C\cr 0 & B \end{pmatrix}$ be $2\times 2$ upper triangular operator matrix…

We provide sufficient and necessary conditions guaranteeing equations $(A+B)^*=A^*+B^*$ and $(AB)^*=B^*A^*$ concerning densely defined unbounded operators $A,B$ between Hilbert spaces. We also improve the perturbation theory of selfadjoint…

Let $X,Y$ be Banach spaces, and fix a linear operator $T \in \mathcal{L}(X,Y)$, and ideals $\mathcal{I}, \mathcal{J}$ on $\omega$. We obtain Silverman--Toeplitz type theorems on matrices $A=(A_{n,k}: n,k \in \omega)$ of linear operators in…

This paper proves two theorems. The first of these simplifies and lends clarity to the previous characterizations of the invariant subspaces of $S$, the operator of multiplication by the coordinate function $z$, on…

Exploiting several $\ell_p$-factorization results for strictly singular operators, we study the strict singularity of the multiplication operator $L_A R_B\colon T\mapsto ATB$ on $\mathcal L(X)$ for various Banach spaces~$X$.

We discuss a notion, originally introduced by Aleman in one variable, of Dirichlet-type space $\mathcal D(\mu_1,\mu_2)$ on the unit bidisc $\mathbb D^2,$ with superharmonic weights related to finite positive Borel measures $\mu_1,\mu_2$ on…

We prove that the bilinear maximal Bochner-Riesz operator $T_*^\lambda$ is bounded from $L^{p_1}(\mathbb R^n)\times L^{p_2}(\mathbb R^n)$ to $L^p(\mathbb R^n)$ for appropriate $(p_1,p_2,p)$ when $\lambda>(4n+3)/5$.

A bounded operator on a real or complex separable infinite-dimensional Banach space $Z$ is universal in the sense of Glasner and Weiss if for every invertible ergodic measure-preserving transformation $T$ of a standard Lebesgue probability…