Diagonalizability of nonautonomous linear systems with bounded continuous coefficients

A linear ODE system with bounded continuous coefficients is studied. Provided that the diagonal terms are “separated” and the off-diagonal terms satisfy a smallness threshold, we present some sufficient conditions for the diagonalizability of the system. The results are valid for any couple of Banach subspaces V,WV,W of BC(R,Cn)BC(R,Cn) admissible for a family of reduced (n−1n−1 dimensional) linear homogeneous systems having exponential dichotomy.