Numerical radius preserving linear maps on Banach algebras
In the literature, linear and nonlinear preservers of the numerical range and numerical radius have been studied extensively. The authors of the paper under review obtain some information concerning numerical radius linear preservers. They show, in particular, that if \(A\) and \(B\) are two unital commutative complex Banach algebras and \(\varphi:A\to B\) is a unital surjective linear map preserving the numerical radius, then \(\varphi\) is an isomorphism.
scientific article; zbMATH DE number 6241493