h-space structure in matrix displacement formulas

A class of spaces of matrices, calledh-spaces, is considered, extending previous results in [R. Bevilacqua, P. Zellini,Closure, commutativity and minmal complexity of some space of matrices, Linear and Multilinear Algebra,25, (1989) 1–25]. These spaces include several known classes of matrix algebras, such as group matrix algebras and Hessenberg algebras and, in particular, certain symmetric closed 1-spaces, which are structurally related to Toeplitz plus Hankel-like matrices. Following the displacement rank technique, these spaces are involved in general displacement decomposition formulas of an arbitrary matrixA. These decompositions lead to a significant representation formula for the inverse of a centrosymmetric Toeplitz plus Hankel matrix.