Let T∈B(H)\documentclass[12pt]{minimal}
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\begin{document}$$ T \in \mathcal {B}(\mathcal {H})$$\end{document} be a bounded linear operator on a Hilbert space H\documentclass[12pt]{minimal}
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\begin{document}$$ \mathcal {H}$$\end{document}, and let T=U|T|\documentclass[12pt]{minimal}
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\begin{document}$$ T = U \vert T \vert $$\end{document} be the polar decomposition of T. For any r>0\documentclass[12pt]{minimal}
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\begin{document}$$r > 0$$\end{document}, the transform Sr(T)\documentclass[12pt]{minimal}
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\begin{document}$$S_{r}(T)$$\end{document} is defined by Sr(T)=U|T|rU\documentclass[12pt]{minimal}
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\begin{document}$$S_{r}(T) = U \vert T \vert ^{r} U$$\end{document}. In this paper, we discuss the transform Sr(T)\documentclass[12pt]{minimal}
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\begin{document}$$S_{r}(T)$$\end{document} of some classes of operators such as p-hyponormal and rank one operators. We provide a new characterization of invertible normal operators via this transform. Afterwards, we investigate when an operator T and its transform Sr(T)\documentclass[12pt]{minimal}
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\begin{document}$$ S_{r}(T) $$\end{document} both have closed ranges, and show that this transform preserves the class of EP operators. Finally, we present some relationships between an EP operator T, its transform Sr(T)\documentclass[12pt]{minimal}
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\begin{document}$$ S_{r}(T)$$\end{document} and the Moore–Penrose inverse T+\documentclass[12pt]{minimal}
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\begin{document}$$ T^{+} $$\end{document}.
