The Rank Ratio Function and the Radius of Comparison
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866913889933852672 |
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| author | Asadi-Vasfi, M. Ali |
| author_facet | Asadi-Vasfi, M. Ali |
| contents | For any given Cuntz semigroup, we introduce a function associated to it, called the ``Rank Ratio Function". This function ensures global control over the oscillation of the rank of any pair of elements in the Cuntz semigroup and, also, plays a very important role in computing the relative radii of comparison of the Cuntz semigroups. Along the way, as we study both the C*-algebraic and algebraic aspects of the relative radius of comparison with a deeper analysis, we introduce another function called the ``Radius of Comparison Function" which provides a method for manufacturing non-classifiable C*-algebras with different relative radii of comparison. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_05764 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Rank Ratio Function and the Radius of Comparison Asadi-Vasfi, M. Ali Operator Algebras Functional Analysis For any given Cuntz semigroup, we introduce a function associated to it, called the ``Rank Ratio Function". This function ensures global control over the oscillation of the rank of any pair of elements in the Cuntz semigroup and, also, plays a very important role in computing the relative radii of comparison of the Cuntz semigroups. Along the way, as we study both the C*-algebraic and algebraic aspects of the relative radius of comparison with a deeper analysis, we introduce another function called the ``Radius of Comparison Function" which provides a method for manufacturing non-classifiable C*-algebras with different relative radii of comparison. |
| title | The Rank Ratio Function and the Radius of Comparison |
| topic | Operator Algebras Functional Analysis |
| url | https://arxiv.org/abs/2505.05764 |