{"paper":{"title":"The compatible Grassmannian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.FA","authors_text":"E. Andruchow, E. Chiumiento, M. E. Di Iorio y Lucero","submitted_at":"2012-08-31T18:26:52Z","abstract_excerpt":"Let $A$ be a positive injective operator in a Hilbert space (\\h, <,>), and denote by [,] the inner product defined by A: [f,g]=<Af,g>. A closed subspace $\\s \\subset \\h$ is called A-compatible if there exists a closed complement for $\\s$, which is orthogonal to $\\s$ with respect to the inner product [,]. Equivalently, if there exists a necessarily unique idempotent operator $Q_\\s$ such that $R(Q_\\s)=\\s$, which is symmetric for this inner product. The compatible Grassmannian $Gr_A$ is the set of all A-compatible subspaces of $\\h$. By parametrizing it via the one to one correspondence $\\s\\leftrig"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.6571","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"}