{"paper":{"title":"Contractive linear preservers of absolutely compatible pairs between C*-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Anil K. Karn, Antonio M. Peralta, Nabin K. Jana","submitted_at":"2018-10-25T14:17:07Z","abstract_excerpt":"Let $a$ and $b$ be elements in the closed ball of a unital C$^*$-algebra $A$ (if $A$ is not unital we consider its natural unitization). We shall say that $a$ and $b$ are domain (respectively, range) absolutely compatible ($a\\triangle_d b$, respectively, $a\\triangle_r b$, in short) if $\\Big| |a| -|b| \\Big| + \\Big| 1-|a|-|b| \\Big| =1$ (resp., $\\Big| |a^*| -|b^*| \\Big| + \\Big| 1-|a^*|-|b^*| \\Big| =1$), where $|a|^2= a^* a$. We shall say that $a$ and $b$ are absolutely compatible ($a\\triangle b$ in short) if they are both range and domain absolutely compatible. In general, $a\\triangle_d b$ (respe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.10886","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":""},"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"}