Related papers: Analytic m-isometries and weighted Dirichlet-type …
In Bergman and Dirichlet spaces, the shift operator is not an isometry, but it is a left invertible operator. In this paper we give conditions on the left invertible operators such that a operator version, in the sense of Rosenblum and…
Here we consider when the difference of two composition operators is compact on the weighted Dirichlet spaces $\mathcal{D}_\alpha$. Specifically we study differences of composition operators on the Dirichlet space $\mathcal{D}$ and $S^2$,…
We prove weighted estimates for singular integral operators which operate on function spaces on a half-line. The class of admissible weights includes Muckenhoupt weights and weights satisfying Sawyer's one-sided conditions. The kernels of…
The purpose of the paper is to study the operators on the weighted Bergman spaces on the unit disk ${\mathbb{D}}$, denoted by $A^{p}_{\lambda,w}({\mathbb{D}})$, that are associated with a class of generalized analytic functions, named the…
We obtain the admissible sets on the unit circle to be the spectrum of a strict $m$-isometry on an $n$-finite dimensional Hilbert space. This property gives a better picture of the correct spectrum of an $m$-isometry. We determine that the…
We study composition operators of characteristic zero on weighted Hilbert spaces of Dirichlet series. For this purpose we demonstrate the existence of weighted mean counting functions associated with the Dirichlet series symbol, and provide…
In this paper, we introduce a general class of weighted spaces of holomorphic Dirichlet series (with real frequencies) analytic in some half-plane and study composition operators on these spaces. In the particular case when the symbol…
Quasi-isometric liftings similar to isometries, for the operators similar to contractions in Hilbert spaces, are investigated. The existence of such liftings is established, and their applications are explored for specific operator classes,…
The aim of this paper is to investigate $m$--isometric composition operators on directed graphs with one circuit. We establish a characterization of $m$--isometries and prove that complete hyperexpansiveness coincides with $2$--isometricity…
We study a class of left-invertible operators which we call weakly concave operators. It includes the class of concave operators and some subclasses of expansive strict $m$-isometries with $m > 2$. We prove a Wold-type decomposition for…
Inspired by recent works on $m$-isometric and $n$-symmetric multivariables operators on Hilbert spaces, in this paper we introduce the class of $(m, n)$-isosymmetric multivariables operators. This new class of operators emerges as a…
In this note we study sub-Hardy Hilbert spaces on which the the action of the operator of multiplication by the coordinate function z is assumed to be weaker than that of an isometry. We identify such operators with a class of weighted…
In this paper, we establish bounds on the norm of multiplication operators on the Bloch space of the unit disk via weighted composition operators. In doing so, we characterize the isometric multiplication operators to be precisely those…
Continuity, compactness, the spectrum and ergodic properties of the differentiation operator are investigated, when it acts in the Fr\'echet space of all Dirichlet series that are uniformly convergent in all half-planes $\{s \in \mathbb{C}…
We develop potential theory for $m$-subharmonic functions with respect to a Hermitian metric on a Hermitian manifold. First, we show that the complex Hessian operator is well-defined for bounded functions in this class. This allows to…
In this article, we consider analytic perturbations of isometries of an analytic Riemannian manifold M. We prove that, under some conditions, a finitely presented group of such small enough perturbations is analytically conjugate on M to…
We prove a local Douglas formula for higher order weighted Dirichlet-type integrals. With the help of this formula, we study the multiplier algebra of the associated higher order weighted Dirichlet-type spaces $\mathcal H_{\pmb\mu},$…
We study boundedness and compactness of composition operators on weighted Bergman spaces of Dirichlet series. Particularly, we obtain in some specific cases, upper and lower bounds of the essential norm of these operators and a criterion of…
We study the isomorphism problem for the multiplier algebras of irreducible complete Pick kernels. These are precisely the restrictions $\mathcal M_V$ of the multiplier algebra $\mathcal M$ of Drury-Arveson space to a holomorphic subvariety…
We discuss the detectable subspaces of an operator. We analyse the relation between the M-function (the abstract Dirichlet to Neumann map) and the resolvent bordered by projections onto the detectable subspaces. The abstract results are…