Werner J. Ricker
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View article: Optimal domain of Volterra operators in Korenblum spaces
Optimal domain of Volterra operators in Korenblum spaces Open
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 dis…
View article: Generalized Cesàro operators in the disc algebra and in Hardy spaces
Generalized Cesàro operators in the disc algebra and in Hardy spaces Open
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 spe…
View article: Measure theoretic aspects of the finite Hilbert transform
Measure theoretic aspects of the finite Hilbert transform Open
The finite Hilbert transform , when acting in the classical Zygmund space (over ), was intensively studied in [8]. In this note, an integral representation of is established via the ‐valued measure for each Borel set . This integral repres…
View article: Measure theoretic aspects of the finite Hilbert transform
Measure theoretic aspects of the finite Hilbert transform Open
The finite Hilbert transform $T$, when acting in the classical Zygmund space $\logl$ (over $(-1,1)$), was intensively studied in \cite{curbera-okada-ricker-log}. In this note an integral representation of $T$ is established via the $L^1(-1…
View article: Generalized Cesàro operators in weighted Banach spaces of analytic functions with sup-norms
Generalized Cesàro operators in weighted Banach spaces of analytic functions with sup-norms Open
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 analyti…
View article: The finite Hilbert transform on $(-1,1)$
The finite Hilbert transform on $(-1,1)$ Open
We present a detailed survey of recent developments in the study of the finite Hilbert transform and its corresponding inversion problem in rearrangement invariant spaces on $(-1,1)$.
View article: Spectral properties of generalized Cesàro operators in sequence spaces
Spectral properties of generalized Cesàro operators in sequence spaces Open
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 $\ell^p$, $c_0$, $c$, $bv_0$,…
View article: Fine spectra and compactness of generalized Cesàro operators in Banach lattices in ${\mathbb C}^{{\mathbb N}_0}$
Fine spectra and compactness of generalized Cesàro operators in Banach lattices in ${\mathbb C}^{{\mathbb N}_0}$ Open
The generalized Cesàro operators $\mathcal{C}_t$, for $t\in[0,1)$, introduced in the 1980's by Rhaly, are natural analogues of the classical Cesàro averaging operator $\mathcal{C}_1$ and act in various Banach sequence spaces $X\subseteq {\…
View article: Convolution in dual Cesàro sequence spaces
Convolution in dual Cesàro sequence spaces Open
We investigate convolution operators in the sequence spaces $d_p$, for $1\le p<\infty$. These spaces, for $p>1$, arise as dual spaces of the \ces sequence spaces $ces_p$ thoroughly investigated by G.~Bennett. A detailed study is also made …
View article: The finite Hilbert transform acting in the Zygmund space LlogL
The finite Hilbert transform acting in the Zygmund space LlogL Open
The finite Hilbert transform T is a singular integral operator which maps the Zygmund space $LlogL:=LlogL(-1,1)$ continuously into $L^1:=L^1(-1,1)$. By extending the Parseval and Poincaré-Bertrand formulae to this setting, it is possible t…
View article: A Fuglede type theorem for Fourier multiplier operators
A Fuglede type theorem for Fourier multiplier operators Open
Let E be a translation invariant Banach function space over an infinite compact abelian group G and Mφ be a Fourier multiplier operator (with symbol φ) acting on E. It is assumed that E has order continuous norm and that E is reflection in…
View article: Fréchet and (LB) sequence spaces induced by dual Banach spaces of discrete Cesàro spaces
Fréchet and (LB) sequence spaces induced by dual Banach spaces of discrete Cesàro spaces Open
The research of J. Bonet was partially supported by the projects MTM2016-76647-P and GV Prometeo/2017/102 (Spain).
View article: Operators acting in sequence spaces generated by Dual Banach spaces of discrete Cesàro spaces
Operators acting in sequence spaces generated by Dual Banach spaces of discrete Cesàro spaces Open
[EN] The dual spaces d(p), 1 < p < infinity, of the discrete Cesaro (Banach) spaces ces(q), 1 < q < infinity, were studied by G. Bennett, A. Jagers and others. These (reflexive) dual Banach spaces induce the non-normable Frechet spaces d(p…
View article: Fréchet and (LB) sequence spaces induced by dual Banach spaces of discrete Cesàro spaces
Fréchet and (LB) sequence spaces induced by dual Banach spaces of discrete Cesàro spaces Open
The Fréchet (resp.\ (LB)) sequence spaces $ces(p+) := \cap_{r > p} ces(r), 1 \leq p < \infty $ (resp.\ $ ces (p-) := \cup_{ 1 < r < p} ces (r), 1 < p \leq \infty),$ are known to be very different to the classical sequence spaces $ \ell_ {p…
View article: Fr\'{e}chet and (LB) sequence spaces induced by dual Banach spaces of discrete Ces\`{a}ro spaces
Fr\'{e}chet and (LB) sequence spaces induced by dual Banach spaces of discrete Ces\`{a}ro spaces Open
The Frechet (resp. (LB)) sequence spaces $ces(p+) := \cap_{r > p} ces(r), 1 \leq p < \infty $ (resp. $ ces (p-) := \cup_{ 1 < r < p} ces (r), 1 < p \leq \infty),$ are known to be very different to the classical sequence spaces $ \ell_ {p+}…
View article: Order spectrum of the Ces\\`aro operator in Banach lattice sequence\n spaces
Order spectrum of the Ces\\`aro operator in Banach lattice sequence\n spaces Open
The discrete Ces\\`aro operator $ C $ acts continuously in various classical\nBanach sequence spaces within $ \\mathbb{C}^{\\mathbb{N}}.$ For the\ncoordinatewise order, many such sequence spaces $ X $ are also complex Banach\nlattices (eg.…
View article: Inversion and extension of the finite Hilbert transform on (-1,1)
Inversion and extension of the finite Hilbert transform on (-1,1) Open
The principle of optimizing inequalities, or their equivalent operator theoretic formulation, is well established in analysis. For an operator, this corresponds to extending its action to larger domains, hopefully to the largest possible s…
View article: On the optimally defined Hardy operator in $L^p$-spaces
On the optimally defined Hardy operator in $L^p$-spaces Open
For each $1<p<\infty$, the optimal extension of the classical Hardy operator from $L^p (\mathbb {R}^+)$ into itself has been identified by Delgado and Soria. By relaxing the target space to be $L^p_{loc} (\mathbb {R}^+)$ we determine the o…
View article: The Cesàro operator in weighted ℓ<sub>1</sub> spaces
The Cesàro operator in weighted ℓ<sub>1</sub> spaces Open
Unlike for , , the discrete Cesàro operator does not map ℓ 1 into itself. We identify precisely those weights w such that does map continuously into itself. For these weights a complete description of the eigenvalues and the spectrum of ar…
View article: The Cesàro operator in weighted $\ell_1$ spaces
The Cesàro operator in weighted $\ell_1$ spaces Open
Unlike for $\ell_p$, $1
View article: The Cesàro operator on power series spaces
The Cesàro operator on power series spaces Open
[EN] The discrete Cesaro operator C is investigated in the class of power series spaces Lambda(0) (alpha) of finite type. Of main interest is its spectrum, which is distinctly different in the cases when Lambda(0) (alpha) is nuclear and wh…
View article: The Cesàro operator on power series spaces
The Cesàro operator on power series spaces Open
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…
View article: On the Radon-Nikodym property in function spaces
On the Radon-Nikodym property in function spaces Open
We exhibit a large class of Banach function spaces which fail to have the Radon-Nikodym property.