@article {
author = {Liu, Na and Luo, Wei and Xu, Qingxiang},
title = {The polar decomposition for adjointable operators on Hilbert $C^*$-modules and centered operators},
journal = {Advances in Operator Theory},
volume = {3},
number = {4},
pages = {855-867},
year = {2018},
publisher = {Tusi Mathematical Research Group (TMRG)},
issn = {2538-225X},
eissn = {2538-225X},
doi = {10.15352/aot.1807-1393},
abstract = {Let $T$ be an adjointable operator between two Hilbert $C^*$-modules and $T^*$ be the adjoint operator of $T$. The polar decomposition of $T$ is characterized as $T=U(T^*T)^\frac12$ and $\mathcal{R}(U^*)=\overline{\mathcal{R}(T^*)}$, where $U$ is a partial isometry, $\mathcal{R}(U^*)$ and $\overline{\mathcal{R}(T^*)}$ denote the range of $U^*$ and the norm closure of the range of $T^*$, respectively. Based on this new characterization of the polar decomposition, an application to the study of centered operators is carried out.},
keywords = {Hilbert $C^*$-module,polar decomposition,centered operator},
url = {http://www.aot-math.org/article_65609.html},
eprint = {http://www.aot-math.org/article_65609_6f7f0f69b19fa35141f279bcbe7bfe9c.pdf}
}