{"paper":{"title":"Correspondence of Kubo-Ando Means over Real Division Algebras and Linearization of Means","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"Allan Merino, Jose Franco","submitted_at":"2026-05-26T21:28:52Z","abstract_excerpt":"In this paper, we establish a bijection between Kubo-Ando operator means defined on the cones $\\mathscr{P}_{n}(\\mathbb{H})$, $\\mathscr{P}_{2n}(\\mathbb{C})$, and $\\mathscr{P}_{4n}(\\mathbb{R})$. This correspondence is induced by the canonical embeddings relating quaternionic, complex, and real positive definite matrices. We investigate several structural and geometric properties preserved by these bijections, including compatibility with functional calculus, invariance under congruence transformations, and behavior with respect to natural metrics on these cones. As an application, we prove that "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.27707","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.27707/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}