{"paper":{"title":"Geometry of unitary orbits of pinching operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.OA","authors_text":"Eduardo Chiumiento, Mar\\'ia E. Di Iorio y Lucero","submitted_at":"2011-05-09T14:33:11Z","abstract_excerpt":"Let I be a symmetrically-normed ideal of the space of bounded operators acting on a Hilbert space H. Let ${p_i}_1 ^w$ $(1\\leq w \\leq \\infty)$ be a family of mutually orthogonal projections on H. The pinching operator associated with the former family of projections is given by P: I --> I, P(x)=\\sum_{i=1}^{w} p_i x p_i. Let UI denote the Banach-Lie group of the unitary operators whose difference with the identity belongs to I. We study several geometric properties of the orbit UI(P)={L_{u} P L_{u^*} : u \\in UI}, where L_u is the left representation of UI on the algebra B(I) of bounded operators"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.1686","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"}