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DOI: 10.23952/cot.2024.10
Received May 27, 2023; Accepted August 10, 2023; Published online October 27, 2023
Abstract. In this paper, we discuss conditions sufficient for the continuity of invariant operators, i.e., generally nonlinear operators commuting with the operator of multiplication by characteristic functions, acting in a large class of spaces of measurable functions over a finite, atomless measure space. Our setting includes, among many others, modular function spaces, Lebesgue spaces, Orlicz and Musielak-Orlicz spaces, variable Lebesgue spaces, and hence extends the scope beyond the normed spaces. Typical examples of invariant operators include superposition operators (also known as Nemytskii operators), multiplication operators and operators constructed from them.
How to Cite this Article:
W.M. Kozlowski, A note on the continuity of invariant operators, Commun. Optim. Theory 2024 (2024) 10.