Distance to regular elements and polar decompositions in a C*-algebra
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866915639233347584 |
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| author | Thiel, Hannes |
| author_facet | Thiel, Hannes |
| contents | We show that the distance from an element of a C*-algebra to the set of regular elements is the infimum of the $δ>0$ for which the $δ$-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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_21391 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Distance to regular elements and polar decompositions in a C*-algebra Thiel, Hannes Operator Algebras Primary 46L05, Secondary 47C15, 47A63 We show that the distance from an element of a C*-algebra to the set of regular elements is the infimum of the $δ>0$ for which the $δ$-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. |
| title | Distance to regular elements and polar decompositions in a C*-algebra |
| topic | Operator Algebras Primary 46L05, Secondary 47C15, 47A63 |
| url | https://arxiv.org/abs/2511.21391 |