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

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 th...

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Bibliographic Details
Published in:Indian journal of pure and applied mathematics Vol. 56; no. 3; pp. 1156 - 1162
Main Authors: Bhat, Archana, Tamminana, Kurmayya
Format: Journal Article
Language:English
Published: Heidelberg Springer Nature B.V 01.09.2025
Subjects:
Hilbert space
Iterative algorithms
Least squares method
Linear operators
Linear systems
Vector space
ISSN:0019-5588, 0975-7465
Online Access:Get full text
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Summary: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.
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ISSN:0019-5588
0975-7465
DOI:10.1007/s13226-025-00830-5