Spectral properties of weighted composition operators on the Bloch and Dirichlet spaces

Ted Eklund; Mikael Lindström; Paweł Mleczko

Displaying similar documents to “Spectral properties of weighted composition operators on the Bloch and Dirichlet spaces”

On the solvability of Dirichlet problem for the weighted p-Laplacian

Dominik Mielczarek, Jerzy Rydlewski, Ewa Szlachtowska (2014)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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In this paper we are concerned with the existence and uniqueness of the weak solution for the weighted p-Laplacian. The purpose of this paper is to discuss in some depth the problem of solvability of Dirichlet problem, therefore all proofs are contained in some detail. The main result of the work is the existence and uniqueness of the weak solution for the Dirichlet problem provided that the weights are bounded. Furthermore, under this assumption the solution belongs to the Sobolev space...

Essential norms of weighted composition operators on the space $ℋ^{\infty}$ of Dirichlet series

Pascal Lefèvre (2009)

Studia Mathematica

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We estimate the essential norm of a weighted composition operator relative to the class of Dunford-Pettis operators or the class of weakly compact operators, on the space $ℋ^{\infty}$ of Dirichlet series. As particular cases, we obtain the precise value of the generalized essential norm of a composition operator and of a multiplication operator.

Centered weighted composition operators via measure theory

Mohammad Reza Jabbarzadeh, Mehri Jafari Bakhshkandi (2018)

Mathematica Bohemica

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We describe the centered weighted composition operators on $L^{2} (Σ)$ in terms of their defining symbols. Our characterizations extend Embry-Wardrop-Lambert’s theorem on centered composition operators.

On weighted composition operators acting between weighted Bergman spaces of infinite order and weighted Bloch type spaces

Elke Wolf (2011)

Annales Polonici Mathematici

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Let ϕ: → and ψ: → ℂ be analytic maps. They induce a weighted composition operator $ψ C_{ϕ}$ acting between weighted Bergman spaces of infinite order and weighted Bloch type spaces. Under some assumptions on the weights we give a characterization for such an operator to be bounded in terms of the weights involved as well as the functions ψ and ϕ

Complex symmetric weighted composition operators on the Hardy space

Cao Jiang, Shi-An Han, Ze-Hua Zhou (2020)

Czechoslovak Mathematical Journal

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This paper identifies a class of complex symmetric weighted composition operators on $H^{2} (𝔻)$ that includes both the unitary and the Hermitian weighted composition operators, as well as a class of normal weighted composition operators identified by Bourdon and Narayan. A characterization of algebraic weighted composition operators with degree no more than two is provided to illustrate that the weight function of a complex symmetric weighted composition operator is not necessarily linear fractional. ...

Weighted composition operators between weighted Banach spaces of holomorphic functions and weighted Bloch type space

Elke Wolf (2009)

Annales Polonici Mathematici

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Let ϕ: → and ψ: → ℂ be analytic maps. They induce a weighted composition operator $ψ C_{ϕ}$ acting between weighted Banach spaces of holomorphic functions and weighted Bloch type spaces. Under some assumptions on the weights we give a necessary as well as a sufficient condition for such an operator to be bounded resp. compact.

Commutant of multiplication operators in weighted Bergman spaces on polydisk

Ali Abkar (2020)

Czechoslovak Mathematical Journal

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We study a certain operator of multiplication by monomials in the weighted Bergman space both in the unit disk of the complex plane and in the polydisk of the $n$ -dimensional complex plane. Characterization of the commutant of such operators is given.

Spectra of weighted composition operators on algebras of analytic functions on Banach spaces

Cheng Yuan, Ze-Hua Zhou (2011)

Czechoslovak Mathematical Journal

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Let $E$ be a complex Banach space, with the unit ball $B_{E}$ . We study the spectrum of a bounded weighted composition operator $u C_{ϕ}$ on $H^{\infty} (B_{E})$ determined by an analytic symbol $ϕ$ with a fixed point in $B_{E}$ such that $ϕ (B_{E})$ is a relatively compact subset of $E$ , where $u$ is an analytic function on $B_{E}$ .

A generalization of the Aleksandrov operator and adjoints of weighted composition operators

Eva A. Gallardo-Gutiérrez, Jonathan R. Partington (2013)

Annales de l’institut Fourier

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A generalization of the Aleksandrov operator is provided, in order to represent the adjoint of a weighted composition operator on $ℋ^{2}$ by means of an integral with respect to a measure. In particular, we show the existence of a family of measures which represents the adjoint of a weighted composition operator under fairly mild assumptions, and we discuss not only uniqueness but also the generalization of Aleksandrov–Clark measures which corresponds to the unweighted case, that is, to the...

The spectral decomposition of weighted shifts and the $A^{p}$ condition

Earl Berkson, T. A. Gillespie (1990)

Colloquium Mathematicae

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New criteria for boundedness and compactness of weighted composition operators mapping into the Bloch space

Flavia Colonna (2013)

Open Mathematics

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Let ψ and φ be analytic functions on the open unit disk $𝔻$ with φ( $𝔻$ ) ⊆ $𝔻$ . We give new characterizations of the bounded and compact weighted composition operators W ψ,ϕ from the Hardy spaces H p, 1 ≤ p ≤ ∞, the Bloch space B, the weighted Bergman spaces A αp, α > − 1,1 ≤ p < ∞, and the Dirichlet space $𝒟$ to the Bloch space in terms of boundedness (respectively, convergence to 0) of the Bloch norms of W ψ,ϕ f for suitable collections of functions f in the respective spaces. We also...

Essential spectra of weighted composition operators with hyperbolic symbols

Olli Hyvärinen, Ilmari Nieminen (2015)

Concrete Operators

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In this paperwe study both the spectra and the essential spectra ofweighted composition operators on Hardy spaces Hp(ⅅ), standard weighted Bergman spaces Apα(ⅅ) and weighted H∞1-type spaces when the symbols are of hyperbolic type

Essential norm of the difference of composition operators on Bloch space

Ke-Ben Yang, Ze-Hua Zhou (2010)

Czechoslovak Mathematical Journal

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Let $ϕ$ and $ψ$ be holomorphic self-maps of the unit disk, and denote by $C_{ϕ}$ , $C_{ψ}$ the induced composition operators. This paper gives some simple estimates of the essential norm for the difference of composition operators $C_{ϕ} - C_{ψ}$ from Bloch spaces to Bloch spaces in the unit disk. Compactness of the difference is also characterized.