{"paper":{"title":"Representations for weighted Moore-Penrose inverses of partitioned adjointable operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Chuanning Song, Qingxiang Xu, Yonghao Chen","submitted_at":"2010-08-04T22:48:18Z","abstract_excerpt":"For two positive definite adjointable operators $M$ and $N$, and an adjointable operator $A$ acting on a Hilbert $C^*$-module, some properties of the weighted Moore-Penrose inverse $A^\\dag_{MN}$ are established. When $A=(A_{ij})$ is $1\\times 2$ or $2\\times 2$ partitioned, general representations for $A^\\dag_{MN}$ in terms of the individual blocks $A_{ij}$ are studied. In case $A$ is $1\\times 2$ partitioned, a unified representation for $A^\\dag_{MN}$ is presented. In the $2\\times 2$ partitioned case, an approach to constructing Moore-Penrose inverses from the non-weighted case to the weighted c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.0887","kind":"arxiv","version":2},"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"}