Characterization of posinormal operators with closed ranges
Vol 3, Issue 1, 2025
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Abstract
Characterization of posinormal operators in terms of their positivity, invertibility and numerical ranges has been done. However, characterization of these operators with regards to their closed ranges remains interesting. In this work, we characterize conditions for posinormal operators to have closed ranges. In particular, we establish an important upper norm bound criterion for posinormal operators. We show that if Q, R are normal operators in PN (H), the set of all posinormal operators acting on a Hilbert space H and suppose that the range of Q is closed with the null space of Q equal to the null space of R, then the range of R is closed. The results of this study are very useful applications in many areas, like image and signal processing. In particular, they are useful in processing signals and images used in facial recognition which are important in the identification of people in places like the airports, thus helping in enhancing security and forensic analysis.
Keywords
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Copyright (c) 2025 Adoyo Alvince Ochieng, Benard Okelo, Priscah Omoke
License URL: https://creativecommons.org/licenses/by/4.0/
Editor-in-Chief
Prof. Youssri Hassan Youssri
Cairo University, Egypt
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