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arXiv · 2402.08972

A class of weighted composition operators whose Range and Null spaces are complemented

Anurag Kumar Patel
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Abstract

In this paper, we prove that the null space of a weighted composition operator on $\ell_p~ (1 \leq p < \infty)$ is a complemented subspace. We also give a necessary and sufficient condition for a weighted composition operator on $\ell_p$ whose range space is of finite co-dimension. Thereafter, we characterize a class of weighted composition operators whose range space is a complemented subspace. Lastly, we characterize weighted composition operators on $\ell_p$ which are Fredholm operators.

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Anurag Kumar Patel. 2024-02-14. A class of weighted composition operators whose Range and Null spaces are complemented. https://arxiv.org/abs/2402.08972

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