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arXiv · 2112.05369

Spectrums and uniform mean ergodicity of weighted composition operators on Fock spaces

Werkaferahu Seyoum·Tesfa Mengestie
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Abstract

For holomorphic pairs of symbols $(u, \psi)$, we study various structures of the weighted composition operator $ W_{(u,\psi)} f= u \cdot f(\psi)$ defined on the Fock spaces $\mathcal{F}_p$. We have identified operators $W_{(u,\psi)}$ that have power bounded and uniformly mean ergodic properties on the spaces. These properties are described in terms of easy to apply conditions relying on the values $|u(0)|$ and $|u(\frac{b}{1-a})|$ where $ a$ and $b$ are coefficients from linear expansion of the symbol $\psi$. The spectrum of the operators are also determined and applied further to prove results about uniform mean ergodicity.

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Werkaferahu Seyoum, Tesfa Mengestie. 2021-12-10. Spectrums and uniform mean ergodicity of weighted composition operators on Fock spaces. https://doi.org/10.1007/s40840-021-01203-x

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