On the image of the mean transform

Fadil Chabbabi; Maëva Ostermann

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arXiv · 2207.13163

On the image of the mean transform

Fadil Chabbabi·Maëva Ostermann

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Abstract

Let $B(H)$ be the algebra of all bounded operators on a Hilbert space $H$. Let $T=V|T|$ be the polar decomposition of an operator $T\in B(H)$. The mean transform of $T$ is defined by $M(T)=\frac{T+|T|V}{2}$. In this paper, we discuss several properties related to the spectrum, the kernel, the image, the polar decomposition of mean transform. Moreover, we investigate the image and preimage by the mean transform of some class of operators as positive, normal, unitary, hyponormal and co-hyponormal operators.

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BibTeX RIS

Fadil Chabbabi, Maëva Ostermann. 2022-07-26. On the image of the mean transform. https://arxiv.org/abs/2207.13163

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