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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1701.03737","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-01-13T17:18:33Z","cross_cats_sorted":[],"title_canon_sha256":"568d9fbceecbb2a013e40ab916d456ecd3589c8ee94f3d11c89d686fce9434be","abstract_canon_sha256":"7c0a048bd84cf85854147cf8a6f16b1f6205b256d72ffe35c0f4b53545dc691f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:54.003066Z","signature_b64":"Xa8hwR+ti8donNIjq1yX8jFDsoNOP7mpu47u03/7/25iyV0UOeJlxAU7GHDit3ijb1UCTz3SVl150N4ESHxXAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9aa42af2f9460edce4899ca688a2e13d1490c18e6ee7c5f20334b99c84429420","last_reissued_at":"2026-05-18T00:52:54.002423Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:54.002423Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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