Papers by Houcine Sadraoui
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