Let \(H_1,H_2\) be two ordered real Hilbert spaces with cones \(C_1,C_2\) respectively. A bounded linear operator \(S:H_1\rightarrow H_2\) is said to be cone nonnegative if \(S(C_1)\subseteq C_2.\) In this short note, we consider weak pseudo-regular splittings of bounded linear operators defined between two Hilbert spaces, and characterize the cone nonnegativity of Moore-Penrose inverses of such operators. We establish a comparison result for spectral radii of iteration operators corresponding to two different weak-pseudo regular splittings of a given bounded linear operator. These results have important applications in least-squares problems, and in iterative algorithms for solving linear systems.
