English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper, we study hyponormal weighed composition operators on the Hardyand weighted Bergman spaces. For functions $\psi \in A(\mathbb{D})$ which arenot the zero function, we characterize all hyponormal compact weightedcomposition operators $C_{\psi,\varphi}$ on $H^{2}$ and $A^{2}_{\alpha}$. Next,we show that for $\varphi \in \mbox{LFT}(\mathbb{D})$, if $C_{\varphi}$ ishyponormal on $H^{2}$ or $A^{2}_{\alpha}$, then $\varphi(z)=\lambda z$, where$|\lambda| \leq 1$ or $\varphi$ is a hyperbolic non-automorphism with$\varphi(0)=0$ and such that $\varphi$ has another fixed point in $\partial\mathbb{D}$. After that, we find the essential spectral radius of $C_{\varphi}$on $H^{2}$ and $A^{2}_{\alpha}$, when $\varphi$ has a Denjoy-Wolff point $\zeta\in \partial \mathbb{D}$. Finally, descriptions of spectral radii are providedfor some hyponormal weighted composition operators on $H^{2}$ and$A^{2}_{\alpha}$.

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