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.
Liu, N., Luo, W., Xu, Q. (2018). The polar decomposition for adjointable operators on Hilbert $C^*$-modules and centered operators. Advances in Operator Theory, 3(4), 855-867. doi: 10.15352/aot.1807-1393
MLA
Na Liu; Wei Luo; Qingxiang Xu. "The polar decomposition for adjointable operators on Hilbert $C^*$-modules and centered operators". Advances in Operator Theory, 3, 4, 2018, 855-867. doi: 10.15352/aot.1807-1393
HARVARD
Liu, N., Luo, W., Xu, Q. (2018). 'The polar decomposition for adjointable operators on Hilbert $C^*$-modules and centered operators', Advances in Operator Theory, 3(4), pp. 855-867. doi: 10.15352/aot.1807-1393
VANCOUVER
Liu, N., Luo, W., Xu, Q. The polar decomposition for adjointable operators on Hilbert $C^*$-modules and centered operators. Advances in Operator Theory, 2018; 3(4): 855-867. doi: 10.15352/aot.1807-1393
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