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

2025/01/17 by Bagarello, Fabio, Inoue, Hiroshi, Triolo, Salvatore · 1 citation
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2501.10545

Abstract

We consider a particular class of sesquilinear forms on a Banach quasi *-algebra (\A[‖.‖],\Ao[‖.‖₀]) which we call \em eigenstates of an element a∈\A, and we deduce some of their properties. We further apply our definition to a family of ladder elements, i.e. elements of \A obeying certain commutation relations physically motivated, and we discuss several results, including orthogonality and biorthogonality of the forms, via GNS-representation.

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