Papers by Houcine Sadraoui
Commuting Toeplitz operators on weighted harmonic Bergman spaces and hyponormality on the Bergman space of the punctured unit disk
AIMS mathematics, 2024
We first describe commuting Toeplitz operators with harmonic symbols on weighted harmonic Bergman... more We first describe commuting Toeplitz operators with harmonic symbols on weighted harmonic Bergman spaces. Then, a sufficient condition for hyponormality on weighted Bergman spaces of the punctured unit disk, when the analytic part of the symbol is a monomial, is shown.
Toeplitz operators and composition operators on the q-Bergman space
Journal of pseudo-differential operators and applications, Feb 10, 2024
A Banach algebra structure on the $q$-Bergman space and related topics
Colloquium Mathematicum, Dec 31, 2022
On hyponormality on the Bergman space of an annulus
Indian Journal of Pure and Applied Mathematics, Dec 17, 2023
In this paper we use the Duhamel product to provide a Ba- nach algebra structure to each of a sca... more In this paper we use the Duhamel product to provide a Ba- nach algebra structure to each of a scale of Bergman spaces over the unit disk, and then carry out many interesting consequences. In particular we characterize cyclic vectors of the Volterra integration operator, and determine its extended eigenvalues and corresponding extended eigenop- erators. We also identify its commutants and point out some intertwin- ing relations between the Volterra integration operator and composition operators.
Hyponormality on an annulus with a general radial weight
Mathematical Methods in the Applied Sciences, 2020
In this work, we consider the hyponormality of Toeplitz operators on the Bergman space of the ann... more In this work, we consider the hyponormality of Toeplitz operators on the Bergman space of the annulus with a general radial weight. We give necessary conditions when the symbol is of the form , where g1 and g2 are analytic on the annulus .
On hyponormality of Toeplitz operators
Rocky Mountain Journal of Mathematics, 2021
Hyponormality of Toeplitz operators and composition operators
A Hilbert space operator T is hyponormal if $T*T-TT*$ is positive. In chapter one we consider hyp... more A Hilbert space operator T is hyponormal if $T*T-TT*$ is positive. In chapter one we consider hyponormality of Toeplitz operators on the Bergman space with a symbol in the class of functions $f+\overline{g},$ where f and g are bounded and analytic in the unit disk. Under a smoothness assumption, we give a necessary condition. We give a sufficient condition in the case f is a monomial and g is a polynomial. In chapter two we study the hyponormality of the adjoints of composition operators, on the Hardy space, with a linear fractional symbol. We give a necessary condition and find an equivalent condition to hyponormality. Using the mentioned equivalent condition we show hyponormality in a special case
Filomat, 2019
A bounded operator T on a Hilbert space is hyponormal if T*T-TT* is positive. We give a necessary... more A bounded operator T on a Hilbert space is hyponormal if T*T-TT* is positive. We give a necessary condition for the hyponormality of Toeplitz operators on weighted Bergman spaces, for a certain class of radial weights, when the symbol is of the form f+g?, where both functions are analytic and bounded on the unit disk. We give a sufficient condition when f is a monomial.
Afrika Matematika, 2019
An operator T on a Hilbert space is hyponormal if T*T-TT* is positive. In this work we consider h... more An operator T on a Hilbert space is hyponormal if T*T-TT* is positive. In this work we consider hyponormality of Toeplitz operators on the Bergman space with a logarithmic weight. Under a smoothness assumption we give a necessary condition when the symbol is of the form f + g with f , g analytic on the unit disk. We also find a sufficient condition when f is a monomial and g a polynomial.
Ufimskii Matematicheskii Zhurnal, 2018
In terms of Berezin symbols, we give new characterizations of the Bloch spaces β¬ and β¬ 0 , Bers-t... more In terms of Berezin symbols, we give new characterizations of the Bloch spaces β¬ and β¬ 0 , Bers-type and the Zygmund-type spaces of analytic functions on the unit disc D in the complex plane C. We discuss some properties of Toeplitz operators on the Bergman space πΏ 2 π (D). We provide a new characterization of certain function space with variable exponents. Namely, given a function Here π· (ππ) denotes the associate diagonal operator on the Hardy-Hilbert space π» 2 defined by the formula π· (ππ) π§ π = π π π§ π (π = 0, 1, 2, . . .).
Open Mathematics
In this work, we consider the hyponormality of Toeplitz operators on the Bergman space of the ann... more In this work, we consider the hyponormality of Toeplitz operators on the Bergman space of the annulus with a logarithmic weight. We give necessary conditions when the symbol is of the form Ο + Ο Β― \varphi +\overline{\psi } , where Ο \varphi and Ο \psi are analytic on the annulus { z β C ; 1 / 2 < β£ z β£ < 1 } \{z\in {\mathbb{C}};\hspace{0.25em}1\hspace{-0.08em}\text{/}\hspace{-0.08em}2\lt | z| \lt 1\} .
Hyponormality of Toeplitz operators on the Bergman space of an annulus
Revista de la UniΓ³n MatemΓ‘tica Argentina
Journal of Function Spaces
A bounded Hilbert space operator T is hyponormal if TβTβTTβ is a positive operator. We consider t... more A bounded Hilbert space operator T is hyponormal if TβTβTTβ is a positive operator. We consider the hyponormality of Toeplitz operators on a weighted Bergman space. We find a necessary condition for hyponormality in the case of a symbol of the form f+gΒ― where f and g are bounded analytic functions on the unit disk. We then find sufficient conditions when f is a monomial.
Hyponormality on an annulus with a weight
Mathematical Methods in the Applied Sciences
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Papers by Houcine Sadraoui