Modulus support functionals, Rajchman measures and peak functions

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).