Positive elements and the \(B^ *\) condition
The basic theory of the ''positive elements'' of a \(B^*\)-algebra is derived from the \(B^*\) condition by a combination of totally elementary argument, the spectral radius formula and the square root lemma. In the process a sort of ''topological norm additivity'' emerges for positive elements. In this note we do two things: we try to properly locate the additivity condition in the development of the theory of positive elements, and we use it to extend ''spectral permanence'' from single elements to more general systems.
scientific article; zbMATH DE number 3988007