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

Fabio Bagarello, Hiroshi Inoue and Salvatore Triolo

Mathematische Nachrichten, 2025, vol. 298, issue 3, 1062-1075

Abstract: We consider a particular class of sesquilinear forms on a Banach quasi *‐algebra (A[∥.∥],A0[∥.∥0])$({\cal A}[\Vert .\Vert],{\cal A}_0[\Vert .\Vert _0])$ that we call eigenstates of an element a∈A$a\in {\cal A}$, and we deduce some of their properties. We further apply our definition to a family of ladder elements, that is, elements of A${\cal A}$ obeying certain commutation relations physically motivated, and we discuss several results, including orthogonality and biorthogonality of the forms, via Gelfand–Naimark–Segal (GNS) representation.

Date: 2025
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