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arXiv · 2204.11633

The polar decomposition of the product of three operators

Dingyi Du·Qingxiang Xu·Shuo Zhao
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Abstract

In the setting of adjointable operators on Hilbert $C^*$-modules, this paper deals with the polar decomposition of the product of three operators. The relationship between the polar decompositions associated with three operators is clarified. Based on this relationship, a formula for the polar decomposition of a multiplicative perturbation of an operator is provided. In addition, some characterizations of the polar decomposition associated with three operators are provided.

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Dingyi Du, Qingxiang Xu, Shuo Zhao. 2022-04-25. The polar decomposition of the product of three operators. https://doi.org/10.1080/03081087.2022.2159920

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