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arXiv · 2204.11577

The $(n+1)$-centered operator on a Hilbert $C^*$-module

Na Liu·Qingxiang Xu·Xiaofeng Zhang
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Abstract

Let $T$ be an adjointable operator on a Hilbert $C^*$-module such that $T$ has the polar decomposition $T=UT|$. For each natural number $n$, $T$ is called an $(n+1)$-centered operator if $T^k=U^k|T^k|$ is the polar decomposition for $1\le k\le n+1$. This paper initiates the study of the $(n+1)$-centered operator via the generalized Aluthge transform and the generalized iterative Aluthge transform. Some new characterizations of the $(n+1)$-centered operator are provided.

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Na Liu, Qingxiang Xu, Xiaofeng Zhang. 2022-04-25. The $(n+1)$-centered operator on a Hilbert $C^*$-module. https://doi.org/10.1007/s43037-022-00240-3

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