Some characterizations of Hermitian Banach algebras
A \(^*\)-algebra \(A\) is said to be Hermitian if \(\mathrm{Sp}(a)\subseteq\mathbb{R}\) for every \(a=a^*\in A\). In this paper, the author proves many new results concerning the properties of Hermitian Banach \(^*\)-algebras. A sample result is Corollary 4.5, which says that, for a Hermitian Banach \(^*\)-algebra \(A\), if \(A_+\) does not contain zero-divisors, then the spectrum of each self-adjoint element of \(A\) is an interval.
scientific article; zbMATH DE number 6838820