Dingyi Du, Qingxiang Xu, Shuo Zhao
Published 2022-04-25Version 1
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.
The effect of perturbations of linear operators on their polar decomposition
A note on the polar decomposition in metric spaces
On the image of the mean transform
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