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Investigates multiplier properties in Lp spaces, suggesting insights for functional analysis.
In this paper, we investigate the structure of the space of multipliers arising from the range of a composition operator cφ, which is induced by the conditional expectation between two Lᵖ(Σ) spaces. After introducing the necessary preliminaries on measure spaces, Lᵖ-spaces, and the conditional expectation operator, we define weighted conditional multipliers and establish conditions under which they generate bounded operators between different Lᵖ(Σ) and Lq(Σ) spaces. Using fundamental properties of conditional expectation, we characterize the structural behavior of these multipliers and explore their relation to injectivity and surjectivity moduli of bounded linear operators. The results provide a precise framework for describing conditional multipliers and open new perspectives for the study of composition operators in functional analysis.
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S. Khalil Sarbaz (2025) studied this question.
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