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Angela A. Albanese

Publications and source records attributed to Angela A. Albanese.

At least 19 recordsLinked to original sources
arXiv2026

Optimal domain of Volterra operators in classes of Banach spaces of analytic functions

A thorough investigation is made of the optimal domain space of generalized Volterra operators, Cesàro operators and other operators when they act in various Banach spaces of analytic functions. Of particular interest is the situation when the operators act in Hardy spaces, Korenblum growth spaces and more general weighted spaces. The optimal domain space may be genuinely larger than the initial domain of the operator, or not. In the former case, the initial space may or may not be dense in the optimal domain space. Sometimes the optimal domain space can be identified with a known Banach space of analytic functions, on other occasions it determines a new space.

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arXiv2026

Optimal domain of Volterra operators in Korenblum spaces

The aim of this article is to study the largest domain space $[T,X]$, whenever it exists, of a given continuous linear operator $T\colon X\to X$, where $X\subseteq H(\mathbb{D})$ is a Banach space of analytic functions on the open unit disc $\mathbb{D}\subseteq \mathbb{C}$. That is, $[T,X]\subseteq H(\mathbb{D})$ is the \textit{largest} Banach space of analytic functions containing $X$ to which $T$ has a continuous, linear, $X$-valued extension $T\colon [T,X]\to X$. The class of operators considered consists of generalized Volterra operators $T$ acting in the Korenblum growth Banach spaces $X:=A^{-γ}$, for $γ>0$. Previous studies dealt with the classical Cesàro operator $T:=C$ acting in the Hardy spaces $H^p$, $1\leq p<\infty$, \cite{CR}, \cite{CR1}, in $A^{-γ}$, \cite{ABR-R}, and more recently, generalized Volterra operators $T$ acting in $X:=H^p$, \cite{BDNS}.

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arXiv2025

Spectral and ergodic properties of the operator $B(r,s)$ over power series spaces $Λ_\infty(α)$ of infinite type and their duals

In this paper, we investigate the spectral and ergodic properties of the linear operator $B(r,s)$ acting on power series spaces $Λ_\infty(α)$ of infinite type and on their strong duals. Precisely, we provide a complete characterization of its fine spectrum and establish necessary and sufficient conditions for the operator to be power bounded and (uniformly) mean ergodic.

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arXiv2025

Topologizability and related properties of the iterates of composition operators in Gelfand-Shilov classes

We analyse the behaviour of the iterates of composition operators defined by polynomials acting on global classes of ultradifferentiable functions of Beurling type which are invariant under the Fourier transform. In particular, we determine the polynomials $ψ$ for which the sequence of iterates of the composition operator $C_ψ$ is topologizable (m-topologizable) acting on certain Gelfand-Shilov spaces defined by mean of Braun-Meise-Taylor weights. We prove that the composition operators $C_ψ$ with $ψ$ a polynomial of degree greater than one are always topologizable in certain settings involving Gelfand-Shilov spaces, just like in the Schwartz space. Unlike in the Schwartz space setting, composition operators $C_ψ$ associated with polynomials $ψ$ are not always $m-$topologizable. We also deal with the composition operators $C_ψ$ with $ψ$ being an affine function acting on $\mathcal{S}_ω(\mathbb{R})$ and find a complete characterization of topologizability and m-topologizability

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arXiv2024

Mean ergodic and related properties of generalized Cesàro operators in BK-sequence spaces

Recent results concerning the linear dynamics and mean ergodicity of compact operators in Banach spaces, together with additional new results, are employed to investigate various spectral properties of generalized Cesàro operators acting in large classes of classical BK-sequence spaces. Of particular interest is to determine the eigenvalues and the corresponding eigenvectors of such operators and to decide whether (or not) the operators are power bounded, mean ergodic and supercyclic.

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arXiv2024

Generalized Cesàro operators in the disc algebra and in Hardy spaces

Generalized Cesàro operators $C_t$, for $t\in [0,1)$, are investigated when they act on the disc algebra $A(\mathbb{D})$ and on the Hardy spaces $H^p$, for $1\leq p \leq \infty$. We study the continuity, compactness, spectrum and point spectrum of $C_t$ as well as their linear dynamics and mean ergodicity on these spaces.

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arXiv2024

Mutual estimates of time-frequency representations and uncertainty principles

In this paper we give different estimates between Lebesgue norms of quadratic time-frequency representations. We show that, in some cases, it is not possible to have such bounds in classical $L^p$ spaces, but the Lebesgue norm needs to be suitably weighted. This leads to consider weights of polynomial type, and, more generally, of ultradifferentiable type, and this, in turn, gives rise to use as functional setting the ultradifferentiable classes. As applications of such estimates we deduce uncertainty principles both of Donoho-Stark type and of local type for representations.

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arXiv2024

Generalized Cesàro operators in weighted Banach spaces of analytic functions with sup-norms

An investigation is made of the generalized Cesàro operators $C_t$, for $t\in [0,1]$, when they act on the space $H(\mathbb{D})$ of holomorphic functions on the open unit disc $\mathbb{D}$, on the Banach space $H^\infty$ of bounded analytic functions and on the weighted Banach spaces $H_v^\infty$ and $H_v^0$ with their sup-norms. Of particular interest are the continuity, compactness, spectrum and point spectrum of $C_t$ as well as their linear dynamics and mean ergodicity.

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arXiv2023

Spectral properties of generalized Cesàro operators in sequence spaces

The generalized Cesàro operators $C_t$, for $t\in [0,1]$, were first investigated in the 1980's. They act continuously in many classical Banach sequence spaces contained in $\mathbb{C}^{\mathbb{N}_0}$, such as $\ell^p$, $c_0$, $c$, $bv_0$, $bv$ and, as recently shown, \cite{CR4}, also in the discrete Cesàro spaces $ces(p)$ and their (isomorphic) dual spaces $d_p$. In most cases $C_t$ ($t\not=1$) is compact and its spectra and point spectrum, together with the corresponding eigenspaces, are known. We study these properties of $C_t$, as well as their linear dynamics and mean ergodicity, when they act in certain non-normable sequence spaces contained in $\mathbb{C}^{\mathbb{N}_0}$. Besides $\mathbb{C}^{\mathbb{N}_0}$ itself, the Fréchet spaces considered are $\ell(p+)$, $ces(p+)$ and $d(p+)$, for $1\leq p<\infty$, as well as the (LB)-spaces $\ell(p-)$, $ces(p-)$ and $d(p-)$, for $1<p\leq\infty$.

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arXiv2021

Spectra and ergodic properties of multiplication and convolution operators on the space $\mathcal{S}(\mathbb{R})$

In this paper we investigate the spectra and the ergodic properties of the multiplication operators and the convolution operators acting on the Schwartz space $\mathcal{S}(\mathbb{R})$ of rapidly decreasing functions, i.e., operators of the form $M_h: \mathcal{S}(\mathbb{R})\to\mathcal{S}(\mathbb{R})$, $f \mapsto h f $, and $C_T\colon \mathcal{S}(\mathbb{R})\to\mathcal{S}(\mathbb{R})$, $f\mapsto T\star f$. Precisely, we determine their spectra and characterize when those operators are power bounded and mean ergodic.

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arXiv2021

Convolutors on $\mathcal{S}_ω(\mathbb{R}^N)$

In this paper we continue the study of the spaces $\mathcal{O}_{M,ω}(\mathbb{R}^N)$ and $\mathcal{O}_{C,ω}(\mathbb{R}^N)$ undertaken in [1]. We determine new representations of such spaces and we give some structure theorems for their dual spaces. Furthermore, we show that $\mathcal{O}'_{C,ω}(\mathbb{R}^N)$ is the space of convolutors of the space $\mathcal{S}_ω(\mathbb{R}^N)$ of the $ω$-ultradifferentiable rapidly decreasing functions of Beurling type (in the sense of Braun, Meise and Taylor) and of its dual space $\mathcal{S}'_ω(\mathbb{R}^N)$. We also establish that the Fourier transform is an isomorphism from $\mathcal{O}'_{C,ω}(\mathbb{R}^N)$ onto $\mathcal{O}_{M,ω}(\mathbb{R}^N)$. In particular, we prove that this isomorphism is topological when the former space is endowed with the strong operator lc-topology induced by $\mathcal{L}_b(\mathcal{S}_ω(\mathbb{R}^N))$ and the last space is endowed with its natural lc-topology.

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arXiv2020

Multipliers on $\mathcal{S}_ω(\mathbb{R}^N)$

The aim of this paper is to introduce and to study the space $\mathcal{O}_{M,ω}(\mathbb{R}^N)$ of the multipliers of the space $\mathcal{S}_ω(\mathbb{R}^N)$ of the $ω$-ultradifferentiable rapidly decreasing functions of Beurling type. We determine various properties of the space $\mathcal{O}_{M,ω}(\mathbb{R}^N)$. Moreover, we define and compare some lc-topologies of which $\mathcal{O}_{M,ω}(\mathbb{R}^N)$ can be naturally endowed.

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arXiv2018

A note on supercyclic operators in locally convex spaces

We treat some questions related to supercyclicity of continuous linear operators when acting in locally convex spaces. We extend results of Ansari and Bourdon and consider doubly power bounded operators in this general setting. Some examples are given.

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arXiv2018

The Cesàro operator on duals of power series spaces of infinite type

A detailed investigation is made of the continuity, spectrum and mean ergodic properties of the Cesàro operator $C$ when acting on the strong duals of power series spaces of infinite type. There is a dramatic difference in the nature of the spectrum of $C$ depending on whether or not the strong dual space (which is always Schwartz) is nuclear.

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arXiv2017

The Cesàro operator in weighted $\ell_1$ spaces

Unlike for $\ell_p$, $1<p\leq\infty$, the discrete Cesàro operator $C$ does not map $\ell_1$ into itself. We identify precisely those weights $w$ such that $C$ does map $\ell_1(w)$ continuously into itself. For these weights a complete description of the eigenvalues and the spectrum of $C$ are presented. It is also possible to identify all $w$ such that $C$ is a compact operator in $\ell_1(w)$. The final section investigates the mean ergodic properties of $C$ in $\ell_1(w)$. Many examples are presented in order to supplement the results and to illustrate the phenomena that occur.

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arXiv2017

The Cesàro operator on power series spaces

The discrete Cesàro operator $\mathsf{C}$ is investigated in the class of power series spaces $Λ_0(α)$ of finite type. Of main interest is its spectrum, which is distinctly different when the underlying Fréchet space $Λ_0(α)$ is nuclear as for the case when it is not. Actually, the nuclearity of $Λ_0(α)$ is characterized via certain properties of the spectrum of $\mathsf{C}$. Moreover, $\mathsf{C}$ is always power bounded, uniformly mean ergodic and, whenever $Λ_0(α)$ is nuclear, also has the property that the range $(I-\mathsf{C})^m(Λ_0(α))$ is closed in $Λ_0(α)$, for each $m\in\mathbb{N}$.

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