h-Space structure in matrix displacement formulas

A class of spaces of matrices, called h-spaces, is considered, extending previous results in [R.Bevilacqua, P. Zellini, Closure, commutativity and minimal complexity of some spaces 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 for an arbitrary matrix A. These decompositions lead to a significant representation formula for the inverse of a centrosymmetric Toeplitz plus Hankel matrix.