Distance to regular elements and polar decompositions in a C*-algebra

Hannes Thiel

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arXiv · 2511.21391

Distance to regular elements and polar decompositions in a C*-algebra

Hannes Thiel

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Abstract

We show that the distance from an element of a C*-algebra to the set of regular elements is the infimum of the $\delta>0$ for which the $\delta$-cut-down of the element admits a polar decomposition within the algebra. This parallels results of Pedersen and Brown-Pedersen describing the distance to invertible and quasi-invertible elements through polar decompositions of cut-downs whose polar parts are unitaries or extreme partial isometries.

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Hannes Thiel. 2025-11-26. Distance to regular elements and polar decompositions in a C*-algebra. https://arxiv.org/abs/2511.21391

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