Non negative Moore-Penrose Iinverses of Unbounded Gram Operators
T. Kurmayya, G. Ramesh
TL;DR
This paper establishes necessary and sufficient conditions for the nonnegativity of Moore-Penrose inverses of unbounded Gram operators in Hilbert spaces, extending previous results for bounded operators.
Contribution
It generalizes existing bounded operator results to unbounded Gram operators, providing new conditions involving convex cones and acuteness.
Findings
Derived conditions for nonnegativity of Moore-Penrose inverses
Extended bounded operator results to unbounded cases
Connected nonnegativity with convex cone acuteness
Abstract
In this paper we derive necessary and sufficient conditions for the nonnegativity of Moore-Penrose inverses of unbounded Gram operators between real Hilbert spaces. These conditions include statements on acuteness of certain closed convex cones. The main result generalizes the existing result for bounded operators [11, Theorem 3.6].
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Taxonomy
TopicsMatrix Theory and Algorithms · Spectral Theory in Mathematical Physics · Holomorphic and Operator Theory