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The polar decomposition for adjointable operators on Hilbert $C^*$-modules and centered operators. (arXiv:1807.01598v1 [math.OA])
来源于:arXiv
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. 查看全文>>