Hermitian and positive \(C\)-semigroups on Banach spaces
Summary: Two classes of operator families, namely \(n\)-times integrated \(C\)-semigroups of hermitian and positive operators on Banach spaces, are studied. By using Gelfand transform and a theorem of Sinclair, we prove some interesting special properties of such \(C\)-semigroups. For instances, every hermitian nondegenerate \(n\)-times integrated \(C\)-semigroup on a reflexive space is the \(n\)-times integral of some hermitian \(C\)-semigroup with a densely defined generator; an exponentially bounded \(C\)-semigroup on \(L^p (\mu)\) \((1<p< \infty)\) dominates \(C\) (a positive injective operator) if and only if its generator \(A\) is bounded, positive, and commutes with \(C\); when \(C\) has dense range, the latter assertion is also true on \(L^1 (\mu)\) and \(C_0 (\Omega)\).
\(n\)-times integrated \(C\)-semigroups of hermitian and positive operators on Banach spaces
scientific article; zbMATH DE number 878493