On the characterization of 2×2 ρ-contraction matrices Original Research Article

We give an explicit description of all ρ-contractive (in Nagy–Foiaimage sense) 2×2 matrices. This description leads to the formulas for ρ-numerical radii when the eigenvalues of such matrices either have equal absolute values or equal (mod π) arguments. We also discuss (natural) generalizations to the case of decomposable operators with at most two-dimensional blocks covering, in particular, the quadratic operators.