Some facts about Quasi-Block Toeplitz matrices

In this paper, we try to find some analytical and approximate solutions for quasiblock Toeplitz (QBT) matrices with some MATLAB commands. We say that, these matrices are semi-infinite block matrices of the kind F = T(F) + E where T(F) = (Fj−k)j,k∈Z, that Fk are m × m matrices such that ∑ i∈Z |Fi | has bounded entries, and E = (ei,j )i,j∈Z+ is a compact correction. Here, we have the norms ∥ F ∥w= ∑ i∈Z ∥ Fi ∥ and ∥ E ∥2 are finite.