Lyapunov theorem of operator pairs in Hilbert space
Yueqing Wang · Journal of Northwest University · 2006
Aim In order to generalize the Lyapunov theorem to the bounded linear operator pairs on Hilbert space.Methods Using the matrix formula of operator under special space decomposition.Results The equivalent statements for the positive stability of operator pairs are obtained,and the spectral description of some certain operator inequality is taken.Conclusion The generalization of Lyapunov theorem holds and becomes a useful tool in giving the equivalent statements of the positive stability of operator pairs.