\(V\)-proximal trustworthy Banach spaces
Summary: In [ibid. 2016, Article ID 1917387, 12 p. (2016; Zbl 1348.49012)], the first author proved the fuzzy sum rule for the \(V\)-proximal subdifferential under some natural assumptions on an equivalent norm of the Banach spaces. In the present paper, we are going to prove that the class of Banach spaces satisfying the fuzzy sum rule is very large and contains all \(L^p\) spaces \(1<p<\infty\) as well as the sequence spaces \(l^p$ $\left( 1 < p < \infty\right)\), the Sobolev spaces \(W^{p,n}$ $(1<p<\infty)\), and the Schatten trace ideals \(\mathbf{C}^p $ $(1<p<\infty)\).
scientific article; zbMATH DE number 7220560
scientific article