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

Na Liu; Qingxiang Xu; Xiaofeng Zhang

doi:10.1007/s43037-022-00240-3

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

Operator Algebras 2024-02-22 v1

Authors: 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.

Keywords

operator theory

Cite

@article{arxiv.2204.11577,
  title  = {The $(n+1)$-centered operator on a Hilbert $C^*$-module},
  author = {Na Liu and Qingxiang Xu and Xiaofeng Zhang},
  journal= {arXiv preprint arXiv:2204.11577},
  year   = {2024}
}