{"paper":{"title":"Essentially orthogonal subspaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Esteban Andruchow, Gustavo Corach","submitted_at":"2017-01-13T17:18:33Z","abstract_excerpt":"We study the set ${\\cal C}$ consisting of pairs of orthogonal projections $P,Q$ acting in a Hilbert space ${\\cal H}$ such that $PQ$ is a compact operator. These pairs have a rich geometric structure which we describe here. They are parted in three subclasses: ${\\cal C}_0$ which consists of pairs where $P$ or $Q$ have finite rank, ${\\cal C}_1$ of pairs such that $Q$ lies in the restricted Grassmannian (also called Sato Grassmannian) of the polarization ${\\cal H}=N(P)\\oplus R(P)$, and ${\\cal C}_\\infty$. Belonging to this last subclass one has the pairs $$ P_If=\\chi_If ,\\ \\ Q_Jf= \\left(\\chi_J \\ha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.03737","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"}