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Mahsa Fatehi

Publications and source records attributed to Mahsa Fatehi.

10 recordsLinked to original sources
arXiv2026

Fredholm multiplication operators on Banach spaces of analytic functions on the open unit disk

We identify properties of a Banach space $\mathcal{B}$ of analytic functions on the open unit disk $\mathbb{D}$ in the complex plane ensuring that a multiplication operator $M_\psi: \mathcal{B} \to\mathcal{B}$ is Fredholm if and only if its symbol $\psi$ is bounded away from $0$ near $\partial \mathbb{D}$. The properties we identify are shared by a wide variety of much-studied spaces, including the Hardy spaces $H^p(\mathbb{D})$, weighted Bergman spaces $A^p_\omega(\mathbb{D})$, Hardy-Sobolev spaces $H^2_\beta(\mathbb{D})$, the spaces $S_j^p(\mathbb{D})$ of functions having $j$-th derivative in $H^p(\mathbb{D})$, and the disk algebra $A$. Thus, as a corollary, our work characterizes Fredholm multiplication operators on these spaces. In addition, we describe the closed, finite-codimensional subspaces of $\mathcal{B}$ that are invariant under $M_z: \mathcal{B} \to \mathcal{B}$ in terms of the zeros that the functions in such subspaces have in common. We discuss connections between these subspaces and the problem of characterizing the Fredholm multiplication operators on $\mathcal{B}$, and we prove that $M_z$ restricted to such a subspace is always cyclic, with a polynomial cyclic vector having degree equal to the codimension of the subspace.

math.FA↗
arXiv2021

Weighted Composition--Differentiation Operator on the Hardy and Weighted Bergman Spaces

In this paper, we consider the sum of weighted composition operator $C_{ψ_{0},φ_{0}}$ and the weighted composition--differentiation operator $D_{ψ_{n},φ_{n},n}$ on the Hardy and weighted Bergman spaces. We describe the spectrum of a compact operator $C_{ψ_{0},φ_{0}}+D_{ψ_{n},φ_{n},n}$ when the fixed point $w$ of $φ_{0}$ and $φ_{n}$ is inside the open unit disk and $ψ_{n}$ has a zero at $w$ of order at least $n$. Also the lower estimate and the upper estimate on the norm of a weighted composition--differentiation operator on the Hardy space $H^{2}$ are obtained. Furthermore, we determine the norm of a composition--differentiation operator $D_{φ,n}$, acting on the Hardy space $H^{2}$, in the case where $φ(z)=bz$ for some complex number $b$ that $|b|<1$.

math.FA↗
arXiv2019

Numerical range of weighted composition operators which contain zero

In this paper, we study when zero belongs to the numerical range of weighted composition operators $C_{ψ,φ}$ on the Fock space $\mathcal{F}^{2}$, where $φ(z)=az+b$, $a,b \in \mathbb{C}$ and $|a|\leq 1$. In the case that $|a|<1$, we obtain a set contained in the numerical range of $C_{ψ,φ}$ and find the conditions under which the numerical range of $C_{ψ,φ}$ contain zero. Then for $|a|=1$, we precisely determine the numerical range of $C_{ψ,φ}$ and show that zero lies in its numerical range.

math.FA↗
arXiv2018

Weighted composition operators on the Fock space

In this paper, we study weighted composition operators on the Fock space. We show that a weighted composition operator is cohyponorma if and only if it is normal. Moreover, we give a complete characterization of closed range weighted composition operators. Finally, we find norms of some weighted composition operators.

math.FA↗
arXiv2018

Complex symmetric weighted composition operators

In this paper we find all complex symmetric weighted composition operators with special conjugations. Then we give spectral properties of these complex symmetric weighted composition operators.

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arXiv2016

Quasinormal and hyponormal weighted composition operators on $H^2$ and $A^2_α$ with linear fractional compositional symbol

In this paper, we study quasinormal and hyponormal composition operators \W with linear fractional compositional symbol $\ph$ on the Hardy and weighted Bergman spaces. We characterize the quasinormal composition operators induced on $H^{2}$ and $A_α^{2}$ by these maps and many such weighted composition operators, showing that they are necessarily normal in all known cases. We eliminate several possibilities for hyponormal weighted composition operators but also give new examples of hyponormal weighted composition operators on $H^2$ which are not quasinormal.

math.FA↗
arXiv2016

Normal, cohyponormal and normaloid weighted composition operators on the Hardy and weighted Bergman spaces

If $ψ$ is analytic on the open unit disk $\mathbb{D}$ and $φ$ is an analytic self-map of $\mathbb{D}$, the weighted composition operator $C_{ψ,φ}$ is defined by $C_{ψ,φ}f(z)=ψ(z)f (φ(z))$, when $f$ is analytic on $\mathbb{D}$. In this paper, we study normal, cohyponormal, hyponormal and normaloid weighted composition operators on the Hardy and weighted Bergman spaces. First, for some weighted Hardy spaces $H^{2}(β)$, we prove that if $C_{ψ,φ}$ is cohyponormal on $H^{2}(β)$, then $ψ$ never vanishes on $\mathbb{D}$ and $φ$ is univalent, when $ψ\not \equiv 0$ and $φ$ is not a constant function. Moreover, for $ψ=K_{a}$, where $|a| < 1$, we investigate normal, cohyponormal and hyponormal weighted composition operators $C_{ψ,φ}$. After that, for $φ$ which is a hyperbolic or parabolic automorphism, we characterize all normal weighted composition operators $C_{ψ,φ}$, when $ψ\not \equiv 0$ and $ψ$ is analytic on $\overline{\mathbb{D}}$. Finally, we find all normal weighted composition operators which are bounded below.

math.FA↗
arXiv2016

Which weighted composition operators are hyponormal on the Hardy and weighted Bergman spaces?

In this paper, we study hyponormal weighed composition operators on the Hardy and weighted Bergman spaces. For functions $ψ\in A(\mathbb{D})$ which are not the zero function, we characterize all hyponormal compact weighted composition operators $C_{ψ,φ}$ on $H^{2}$ and $A^{2}_α$. Next, we show that for $φ\in \mbox{LFT}(\mathbb{D})$, if $C_φ$ is hyponormal on $H^{2}$ or $A^{2}_α$, then $φ(z)=λz$, where $|λ| \leq 1$ or $φ$ is a hyperbolic non-automorphism with $φ(0)=0$ and such that $φ$ has another fixed point in $\partial \mathbb{D}$. After that, we find the essential spectral radius of $C_φ$ on $H^{2}$ and $A^{2}_α$, when $φ$ has a Denjoy-Wolff point $ζ\in \partial \mathbb{D}$. Finally, descriptions of spectral radii are provided for some hyponormal weighted composition operators on $H^{2}$ and $A^{2}_α$.

math.FA↗