{"paper":{"title":"The minimal and maximal symmetries for $J$-contractive projections","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Jiajia Niu, Jiaxin Zhang, Xiaomei Cai, Yuan Li","submitted_at":"2018-10-12T07:06:55Z","abstract_excerpt":"In this paper, we firstly character the structures of symmetries $J$ such that a projection $P$ is $J$-contractive. Then the minimal and maximal elements of the symmetries $J$ with $P^{\\ast}JP\\leqslant J$(or $JP\\geqslant0)$ are given. Moreover, some formulas between $P_{(2I-P-P^{\\ast})^{+}}$ $(P_{(2I-P-P^{\\ast})^{-}})$ and $P_{(P+P^{\\ast})^-}$ $(P_{(P+P^{\\ast})^+})$ are established."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.05381","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"}