On Weak Pseudo-regular Splittings of Bounded Linear Operators and Nonnegative Moore-Penrose Inverses - Bhat, Archana; Tamminana, Kurmayya (Indian journal of pure and applied mathematics, 2025)
Let H1,H2 be two ordered real Hilbert spaces with cones C1,C2 respectively. A bounded linear operator S:H1→H2 is said to be cone nonnegative if S(C1)⊆C2. 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.