Isometric and selfadjoint operators on a vector space with nondegenerate diagonalizable form (Q2174409)

Canonical forms of isometric, selfadjoint and skewadjoint operators on a complex or real vector space with nondegenerate symmetric or Hermitian form are well studied in the literature. Let \(V\) be a vector space over a field \(F\) with scalar product given by a nondegenerate sesquilinear form whose matrix is diagonal in some basis. For \(F = \mathbb{C}\), the authors provide canonical matrices of isometric and selfadjoint operators on \(V\) using known classifications of isometric and selfadjoint operators on a complex vector space with nondegenerate Hermitian form. If \(F\) is a field of characteristic different from 2, they obtain canonical matrices of isometric, selfadjoint, and skewadjoint operators on \(V\) up to symmetric and Hermitian forms over finite extensions of \(F\). The article is well written and many useful results are discussed. It can be useful for researchers working in the field of operator theory and functional analysis.