arXiv subjects

Mahmood Haji Shaabani

Publications and source records attributed to Mahmood Haji Shaabani.

3 recordsLinked to original sources

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↗