<?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%">MEKKAOUI, FARIDA</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%">CLASSES OF OPERATORS ASSOCIATED WITH (f,g)-ALUTHGE TRANSFORMS</style></title><secondary-title><style face="normal" font="default" size="100%">Asia Pacific Journal of Mathematics</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2025</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://apjm.apacific.org/PDFs/12-57.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">12</style></volume><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 Hilbert space H with the polar decomposition T =U|T|. The(f,g)-Aluthge transform of the operator T, denoted by ∆f,g(T), is defined as ∆f,g(T) = f(|T|)Ug(|T|), wheref andg botharenon-negativecontinuousfunctionson[0,∞[suchthatf(x)g(x) = x, for all x ≥ 0. In this paper, firstly, we investigate the relationship between this transform and several classes of operators as quasi-normal, normal, positive, nilpotent and closed range operators. Secondly, we show that under some conditions the (f,g)-Aluthge transform possesses the polar decomposition. Lastly, we provide a characterization of binormal operators from the viewpoint of the polar decomposition and the (f, g)-Aluthge transform. 2020 Mathematics Subject Classification. 47A05; 47B49. Key words and phrases. (f,g)-Aluthge transform; quasinormal operato; Polar decomposition; binormal operators.
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