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arXiv · 1809.05118

Rigidity of weighted composition operators on $H^p$

Mikael Lindström·Santeri Miihkinen·Pekka J. Nieminen
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Abstract

We show that every non-compact weighted composition operator $f \mapsto u\cdot (f\circ\phi)$ acting on a Hardy space $H^p$ for $1 \leq p < \infty$ fixes an isomorphic copy of the sequence space $\ell^p$ and therefore fails to be strictly singular. We also characterize those weighted composition operators on $H^p$ which fix a copy of the Hilbert space $\ell^2$. These results extend earlier ones obtained for unweighted composition operators.

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Mikael Lindström, Santeri Miihkinen, Pekka J. Nieminen. 2018-09-13. Rigidity of weighted composition operators on $H^p$. https://arxiv.org/abs/1809.05118

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