Ascent and Descent of Weighted Composition Operators on Lorentz spaces

2024/04/25 by Gopal Datt, Datt, Gopal, Daljeet Singh Bajaj +1
Mathematics · #47B37 #47B38 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Primary: 47B33 #Secondary: 46E30

paper · pdf · doi:10.48550/arxiv.2404.16491

openalex publication_date 2024/04/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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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