Sesquilinear forms as eigenvectors in quasi *‐algebras, with an application to ladder elements

Abstract We consider a particular class of sesquilinear forms on a Banach quasi *‐algebra that we call eigenstates of an element , and we deduce some of their properties. We further apply our definition to a family of ladder elements, that is, elements of obeying certain commutation relations physically motivated, and we discuss several results, including orthogonality and biorthogonality of the forms, via Gelfand–Naimark–Segal (GNS) representation.