The ALM-Framework in the Theory of Multivariate Operator Means
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912432232857600 |
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| author | Hoshina, Dante Wada, Shuhei |
| author_facet | Hoshina, Dante Wada, Shuhei |
| contents | In this paper, we generalize the ALM-procedure introduced by Ando, Li, and Mathias for extending operator geometric means to multiple variables. We prove that the generalized procedure preserves all the properties required by the axioms of operator means, along with several additional desirable properties. Moreover, we examine the self-adjointness of the canonical geometric mean constructed through this procedure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_13098 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The ALM-Framework in the Theory of Multivariate Operator Means Hoshina, Dante Wada, Shuhei Functional Analysis 47A63, 47A64 In this paper, we generalize the ALM-procedure introduced by Ando, Li, and Mathias for extending operator geometric means to multiple variables. We prove that the generalized procedure preserves all the properties required by the axioms of operator means, along with several additional desirable properties. Moreover, we examine the self-adjointness of the canonical geometric mean constructed through this procedure. |
| title | The ALM-Framework in the Theory of Multivariate Operator Means |
| topic | Functional Analysis 47A63, 47A64 |
| url | https://arxiv.org/abs/2506.13098 |