Generalized domination in ordered Banach algebras: an introduction
Volume 177 / 2024
Colloquium Mathematicum 177 (2024), 81-98
MSC: Primary 46H10; Secondary 47A10, 47B65
DOI: 10.4064/cm9452-12-2024
Published online: 2 January 2025
Abstract
Let $A$ be an ordered Banach algebra and $a,b \in A$ such that $0 \leq a \leq b$. The domination problem involves finding natural conditions under which properties of $b$ will be inherited by $a$. In this paper we consider the more general problem where the assumption $0 \leq a \leq b$ is replaced by the weaker condition $\pm a \leq b$.
