Related papers: The Ces\`aro operator in weighted $\ell_1$ spaces

In this article, we consider the singular value asymptotics of compositions of compact linear operators mapping in the real Hilbert space of quadratically integrable functions over the unit interval. Specifically, the composition is given…

We describe holomorphic functions and fractional powers of Ces\'{a}ro operators in $L^2(\mathbb{R})$, $L^2(\mathbb{R}_+)$, and $L^2[0,1]$. Logarithms of Ces\'{a}ro operators are introduced as well and their spectral properties are studied.…

It is proved that every operator from a weak$^*$-closed subspace of $\ell_1$ into a space $C(K)$ of continuous functions on a compact Hausdorff space $K$ can be extended to an operator from $\ell_1$ to $C(K)$.

Let $\mu$ be a finite positive Borel measure on the interval $[0, 1)$ and $f(z)=\sum_{n=0}^{\infty}a_{n}z^{n} \in H(\mathbb{D})$. The Ces\`aro-like operator is defined by $$ \mathcal {C}_{\mu}…

This paper explores various classes of invariant subspaces of the classical Ces\`{a}ro operator $C$ on the Hardy space $H^2$. We provide a new characterization of the finite co-dimensional $C$-invariant subspaces, based on earlier work of…

We consider the composition of operators with non-closed range in Hilbert spaces and how the nature of ill-posedness is affected by their composition. Specifically, we study the \mbox{Hausdorff-,} Ces\`{a}ro-, integration operator, and…

We derive faithful inclusions of C*-algebras from a coend-type construction in unitary tensor categories. This gives rise to different potential notions of discreteness for an inclusion in the non-irreducible case, and provides a unified…

In this paper we solve a long standing problem about the bilinear $T1$ theorem to characterize the (weighted) compactness of bilinear Calder\'{o}n-Zygmund operators. Let $T$ be a bilinear operator associated with a standard bilinear…

We study several notions of boundedness for operators. It is known that any power bounded operator is absolutely Ces\`aro bounded and strong Kreiss bounded (in particular, uniformly Kreiss bounded). The converses do not hold in general. In…

In this article we study the Ces\`{a}ro operator $$ \mathcal{C}(f)(z)=\frac{1}{z}\int_{0}^{z}f(\zeta)\,d\zeta, $$ and its companion operator $\mathcal{T}$ on Hardy spaces of the upper half plane. We identify $\mathcal{C}$ and $\mathcal{T}$…

In this paper, we introduce and investigate the notion of the Ces\'aro operator $C_{\mathscr T}$ on a rooted directed tree $\mathscr T.$ When $\mathscr T$ is the rooted tree with no branching vertex, then $C_{\mathscr T}$ is unitarily…

We consider $\ell^r$ extensions of Calderon-Zygmund operators on weighted spaces $L^p(w)$ with $w$ an $A_p$ weight and $1 < p < \infty$. We give quantitative estimates of these operators' norm in terms of a given weight's $A_p$…

In this paper we prove weighted $\ell^p$-inequalities for variation and oscillation operators defined by semigroups of operators associated with discrete Jacobi operators. Also, we establish that certain maximal operators involving sums of…

This paper explores a version of the classical Ces`aro integral operator for the Lebesgue space L2(0, 1) where we discuss its norm, adjoint, spectral properties, and invariant subspaces. An important tool will be semigroups of weighted…

Let $C_\varphi$ be a composition operator acting on the Hardy space of the unit disc $H^p$ ($1\leq p < \infty$), which is embedded in a $C_0$-semigroup of composition operators $\mathcal{T}=(C_{\varphi_t})_{t\geq 0}.$ We investigate whether…

In this paper, we characterize supercyclic weighted composition operators on a large class of solid Banach function spaces, in particular on Lebesgue, Orlicz and Morrey spaces. Also, we characterize supercyclic weighted composition…

Let $\mathcal{T}^*$ be the semi-group maximal function associated to the Schr\"odinger operator $-\Delta+V(x)$ with $V$ satisfying an appropriate reverse H\"{o}lder inequality. In this paper, we show that the commutator of $\mathcal{T}^*$…

We study power boundedness and related properties such as mean ergodicity for (weighted) composition operators on function spaces defined by local properties. As a main application of our general approach we characterize when (weighted)…

For the weight function $\prod_{i=1}^{d+1}|x_i|^{2\k_i}$ on the unit sphere, sharp local estimates of the orthogonal projection operators are obtained and used to prove the convergence of the Ces\`aro $(C,\delta)$ means in the weighted…

The discrete Ces\`aro operator $ C $ acts continuously in various classical Banach sequence spaces within $ \mathbb{C}^{\mathbb{N}}.$ For the coordinatewise order, many such sequence spaces $ X $ are also complex Banach lattices (eg. $c_0,…