Discontinuous maps from Lipschitz algebras
The existence of homomorphisms and derivations from the little Lipschitz algebra lip\(_\alpha(X)=\{f\in\) Lip\(_\alpha(X): | f(t)-f(s)| /d(t,s)^\alpha\to 0\) as \(d(t,s)\to 0\}\subset \) Lip\(_\alpha(X)\), \(0<\alpha<1\), on an infinite compact metric space \(X\), that are discontinuous on every dense subalgebra is established in this article. As a corollary it is shown that given a \(\beta\in[\alpha,\) min\(\{2\alpha,1\})\) there are homomorphisms and derivations that are discontinuous with respect to the Lipschitz norm on lip\(_\delta(X)\) for all \(\delta\in[\alpha, \beta]\). The article is a continuation of a previous paper by the same author.
scientific article; zbMATH DE number 1199817
scientific article