In this paper, we prove that the null space of a weighted composition operator on ₚ~ (1 ≤ p < ∞) is a complemented subspace. We also give a necessary and sufficient condition for a weighted composition operator on 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 ₚ which are Fredholm operators.
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Anurag Kumar Patel (2024) studied this question.
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