On Weak Pseudo-regular Splittings of Bounded Linear Operators and Nonnegative Moore-Penrose Inverses

Archana Bhat () and Kurmayya Tamminana ()
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Archana Bhat: Sreenidhi University
Kurmayya Tamminana: National Institute of Technology Andhra Pradesh

Indian Journal of Pure and Applied Mathematics, 2025, vol. 56, issue 3, 1156-1162

Abstract: Abstract Let $$H_1,H_2$$ H 1 , H 2 be two ordered real Hilbert spaces with cones $$C_1,C_2$$ C 1 , C 2 respectively. A bounded linear operator $$S:H_1\rightarrow H_2$$ S : H 1 → H 2 is said to be cone nonnegative if $$S(C_1)\subseteq C_2.$$ S ( C 1 ) ⊆ 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.

Keywords: Moore-Penrose inverse; Cone nonnegativity; Proper splitting of operators; Comparison results.; 15A09; 47B02; 47B65 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s13226-025-00830-5

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