Related papers: The Ces\`aro operator on power series spaces

We characterize the topologizability and power boundedness of convolution and dual convolution operators on power series spaces. We determine necessary conditions for a Toeplitz operator to be m-topologizable, and power bounded on…

We describe the closed, densely defined linear transformations commuting with a given operator T of class C_0 in terms of bounded operators in {T}'. Our results extend those of Sarason for operators with defect index 1, and Martin in the…

The spectral theory for operator pencils and operator differential-algebraic equations is studied. Special focus is laid on singular operator pencils and three different concepts of singularity of operator pencils are introduced. The…

A C*-algebra is determined to a great extent by the partial order of its commutative C*-algebras. We study order-theoretic properties of this dcpo. Many properties coincide: the dcpo is, equivalently, algebraic, continuous, meet-continuous,…

We are concerned with the non-normal Schr\"odinger operator $$ H=-\Delta+V $$ on $ L^2(\mathbb R^n)$, where $V\in W^{1,\infty}_{\text{loc}}(\mathbb{R}^n)$ and $\operatorname{Re} (V(x))\ge c|x|^2-d$ for some $c,d>0$. The spectrum of this…

A set of complex numbers $\Lambda=\{\lambda_n,\mu_n\}_{n=1}^{\infty}$ with multiple terms \[ \{\lambda_n,\mu_n\}_{n=1}^{\infty}:= \{\underbrace{\lambda_1,\lambda_1,\dots,\lambda_1}_{\mu_1 - times},…

We obtaine the full characterization of proper closed invariant subspaces of a generalized backward shift operator (Pommiez operator) in the Frechet space of all holomorphic functions on a simply connected domain $\Omega$ of the complex…

We investigate the structure of norm-preserving and linear but not necessarily surjective operators on variable-exponent, discrete Lebesgue spaces. A certain class of isometries, novel to this work, are especially considered; this class…

We consider the Schr\"odinger operator $\mathcal L_{\alpha}$ on the half-line with a periodic background potential and a perturbation which consists of two parts: a summable potential and the slowly decaying Wigner--von Neumann potential…

It is shown that if $\alpha ,\zeta $ are ordinals such that $1\leq \zeta <\alpha <\zeta \omega ,$ then there is an operator from $C(\omega ^{\omega ^\alpha })$ onto itself such that if $Y$ is a subspace of $C(\omega ^{\omega ^\alpha })$…

We suggest a new version of the notion of $\rho$-dilation ($\rho>0$) of an $N$-tuple $\mathbf{A}=(A_1,...,A_N)$ of bounded linear operators on a common Hilbert space. We say that $\mathbf{A}$ belongs to the class $C_{\rho,N}$ if…

We investigate the spectral properties of the volume operator in quantum gravity in the framework of a previously introduced lattice discretization. The presence of a well-defined scalar product in this approach permits us to make definite…

The space of linear differential operators on a smooth manifold $M$ has a natural one-parameter family of $Diff(M)$ (and $Vect(M)$)-module structures, defined by their action on the space of tensor-densities. It is shown that, in the case…

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…

Rhaly operators, as generalizations of the Ces\`aro operator, are studied from the standpoint of view of spectral theory and invariant subspaces, extending previous results by Rhaly and Leibowitz to a framework where generalized Ces\`aro…

Given a curve C on a projective nonsingular rational surface S, over an algebraically closed field of characteristic zero, we are interested in the set Omega_C of linear systems Lambda on S satisfying C is in Lambda, dim Lambda > 0, and the…

For a quasinilpotent operator $T$ on a separable Hilbert space $\mathcal{H}$, Douglas and Yang define $k_x=\limsup\limits_{\lambda\rightarrow 0}\frac{\ln\|(\lambda-T)^{-1}x\|}{\ln\|(\lambda-T)^{-1}\|}$ for each nonzero vector $x$, and call…

If $T$ is a (densely defined) self-adjoint operator acting on a complex Hilbert space $\mathcal{H}$ and $I$ stands for the identity operator, we introduce the delta function operator $\lambda \mapsto \delta \left(\lambda I-T\right) $ at…

The paper is devoted to the study of the essential spectrum of discrete Schr\"{o}dinger operators on the lattice $\mathbb{Z}^{N}$ by means of the limit operators method. This method has been applied by one of the authors to describe the…

For an exotic locally compact Hausdorff space $L$, constructed under the assumption of the Ostaszewski's $\clubsuit$-principle, and a countable ordinal space $\alpha$, we prove that all operators defined on $C_0(\alpha\times L)$ are as…