@article {101770,
	title = {CLASSES OF OPERATORS ASSOCIATED WITH (f,g)-ALUTHGE TRANSFORMS},
	journal = {Asia Pacific Journal of Mathematics},
	volume = {12},
	number = {57},
	year = {2025},
	abstract = {
	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,$\infty$[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.

},
	url = {https://apjm.apacific.org/PDFs/12-57.pdf},
	author = {MEKKAOUI, FARIDA and Menkad, Safa}
}
