The aim of this article is to detect the ascent and descent of weighted composition operators on Lorentz spaces. We investigate the conditions on the measurable transformation T and the complex-valued measurable function u defined on measure space (X, A, μ) that cause the weighted composition operators on Lorentz space $L(p, q)$, 1 < p ≤ ∞, 1 ≤ q ≤ ∞ to have finite or infinite ascent (descent). We also give a number of examples in support of our findings.
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Datt et al. (2024) studied this question.
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