Authors : Philemon Murimi; Sammy Musundi; Dr. Peter Muiruri

Volume/Issue : Volume 11 - 2026, Issue 6 - June

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Google Scholar : https://tinyurl.com/tvs3t3u

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DOI : https://doi.org/10.38124/ijisrt/26jun1729

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Abstract : interrupter for the operator T. This paper studied the closed-ness aspect and commutativ-ity properties of this operator and the related class of m-hyponormal operator in Hilbert space. The results showed that if T is n-posinormal operator then,T∗ is also n-posinormal operator.The results also were extended to the class of m-hyponormal operators. Similarly, the results showed that, if T is n-posinormal operator in Hilbert space H, then any operator S, unitary equivalent to T, is also n-posinormal operator. Furthermore, the results showed that the class of nposinormal and m-hyponormal operators is closed in the operator norm topology. To achieve these results, the properties of linear operators, normal operators and posinormal operators were extended to the higher order n-posinormal and mhyponormal operators.

Keywords : Normal Operators, Hyponormal Operators, Adjoints, N Power Normal Opera-Tors, M-Hyponormal Operators and NPosinormal Operators.

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