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Autumn 2018 The polar decomposition for adjointable operators on Hilbert $C^*$-modules and centered operators
Na Liu‎, Wei Luo, Qingxiang Xu
Adv. Oper. Theory 3(4): 855-867 (Autumn 2018). DOI: 10.15352/aot.1807-1393

Abstract

‎‎‎Let $T$ be an adjointable operator between two Hilbert $C^*$-modules‎, ‎and let $T^*$ be the adjoint operator of $T$‎. ‎The polar decomposition of $T$ is characterized as $T=U(T^*T)^\frac{1}{2}$ 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.

Citation

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Na Liu‎. Wei Luo. Qingxiang Xu. "The polar decomposition for adjointable operators on Hilbert $C^*$-modules and centered operators." Adv. Oper. Theory 3 (4) 855 - 867, Autumn 2018. https://doi.org/10.15352/aot.1807-1393

Information

Received: 27 June 2018; Accepted: 12 July 2018; Published: Autumn 2018
First available in Project Euclid: 27 July 2018

MathSciNet: MR3856178
Digital Object Identifier: 10.15352/aot.1807-1393

Subjects:
Primary: 46L08
Secondary: 47A05

Rights: Copyright © 2018 Tusi Mathematical Research Group

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Vol.3 • No. 4 • Autumn 2018
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