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

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  • Fabio Bagarello
  • Hiroshi Inoue
  • Salvatore Triolo

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.

Suggested Citation

  • Fabio Bagarello & Hiroshi Inoue & Salvatore Triolo, 2025. "Sesquilinear forms as eigenvectors in quasi *‐algebras, with an application to ladder elements," Mathematische Nachrichten, Wiley Blackwell, vol. 298(3), pages 1062-1075, March.
    • Handle: RePEc:bla:mathna:v:298:y:2025:i:3:p:1062-1075
    DOI: 10.1002/mana.202400291
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