Eigenstates on $O^\ast$-algebras with an application to ladder operators

Abstract

Following some recent results, we consider here a particular class of states on a $O^\ast$-algebra $\M$ which we call {\em eigenstates of an element} $A\in\M$, and we deduce some of their properties. Then, we apply our definition to a family of ladder elements, i.e. elements of $\M$ obeying certain algebraic (commutation) relations which are physically motivated, and we discuss several results for these states