<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Elgues, Anissa</style></author><author><style face="normal" font="default" size="100%">Menkad, Safa</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ON THE CLASS OF n-NORMAL OPERATORS AND MOORE-PENROSE INVERSE</style></title><secondary-title><style face="normal" font="default" size="100%">Advances in Mathematics: Scientific Journal</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2023</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://www.research-publication.com/amsj/uploads/papers/vol-12/iss-01/AMSJ-2023-N01-01.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">12</style></volume><pages><style face="normal" font="default" size="100%">1–16</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p style=&quot;text-align: justify;&quot;&gt;
	Let T ∈ B(H) be a bounded linear operator on a complex Hilbert space H. For n ∈ N, an operator T ∈ B(H) is said to be n-normal if T nT ∗ = T ∗T n. In this paper we investigate a necessary and sufficient condition for the n-normality of ST and T S, where S, T ∈ B(H). As a consequence, we generalize Kaplansky theorem for normal operators to n-normal operators. Also, In this paper, we provide new characterizations of n-normal operators by certain conditions involving powers of Moore-Penrose inverse.
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