Abstract
In 2000 Victor Lomonosov suggested a counterexample to the complex version of the Bishop–Phelps theorem on modulus support functionals. We discuss the \(c_0\)-analog of that example and demonstrate that the set of sup-attaining functionals is non-trivial, thus answering an open question, asked in Kadets et al. (The mathematical legacy of Victor Lomonosov. Operator theory. Advances in analysis and geometry 2. De Gruyter, Berlin, 157–187, 2020).
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The research of the second author was done in the framework of the Ukrainian Ministry of Education and Science Research Program 0118U002036, was partially supported by the project PGC2018-093794-B-I00 (MCIU/AEI/FEDER, UE) and on the final stage by the National Research Foundation of Ukraine funded by Ukrainian State budget in frames of Project 2020.02/0096 “Operators in infinite-dimensional spaces: the interplay between geometry, algebra and topology”
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Golinskii, L., Kadets, V. Modulus support functionals, Rajchman measures and peak functions. RACSAM 115, 52 (2021). https://doi.org/10.1007/s13398-020-00974-5
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DOI: https://doi.org/10.1007/s13398-020-00974-5