Redheffer's theorem revisited

Based on the Ben Artzi-Gohberg result concerning the equivalence between the invertibility of theL2-operator\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$(Tx)(t) = \dot x(t) - A(t)x(t)$$ \end{document} and the exponential dichotomic evolution defined byA(t), the time-varying counterpart of the Redheffer theorem is considered under relaxed conditions.