{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:PFBGL3SZDNNWOSZG4DUWASJOQX","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"8352d4eafb8bab9fc52798c9d532bc296e39730e9dc4cb4c02293a5085891152","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-09-25T15:18:15Z","title_canon_sha256":"ecbf3106f45952b9f0a1298c823da5b39816008fe9fa7eca107624e3aac47e80"},"schema_version":"1.0","source":{"id":"1709.08547","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.08547","created_at":"2026-05-18T00:03:50Z"},{"alias_kind":"arxiv_version","alias_value":"1709.08547v2","created_at":"2026-05-18T00:03:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.08547","created_at":"2026-05-18T00:03:50Z"},{"alias_kind":"pith_short_12","alias_value":"PFBGL3SZDNNW","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"PFBGL3SZDNNWOSZG","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"PFBGL3SZ","created_at":"2026-05-18T12:31:37Z"}],"graph_snapshots":[{"event_id":"sha256:1445c68cfb33244713fdcb0a161c6a30830911532a77649b743038c345d2f803","target":"graph","created_at":"2026-05-18T00:03:50Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We present a completely new structure theoretic approach to the dilation theory of linear operators. Our main result is the following theorem: if $X$ is a super-reflexive Banach space and $T$ is contained in the weakly closed convex hull of all invertible isometries on $X$, then $T$ admits a dilation to an invertible isometry on a Banach space $Y$ with the same regularity as $X$. The classical dilation theorems of Sz.-Nagy and Akcoglu-Sucheston are easy consequences of our general theory.","authors_text":"Jochen Gl\\\"uck, Stephan Fackler","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-09-25T15:18:15Z","title":"A Toolkit for Constructing Dilations on Banach Spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.08547","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:ff00fbe2e3c911643e07c5a3d231cd30ec114b2b7ceeb478e57180c08f4eb3b8","target":"record","created_at":"2026-05-18T00:03:50Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"8352d4eafb8bab9fc52798c9d532bc296e39730e9dc4cb4c02293a5085891152","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-09-25T15:18:15Z","title_canon_sha256":"ecbf3106f45952b9f0a1298c823da5b39816008fe9fa7eca107624e3aac47e80"},"schema_version":"1.0","source":{"id":"1709.08547","kind":"arxiv","version":2}},"canonical_sha256":"794265ee591b5b674b26e0e960492e85c681f4b012e0dd0cec89898d418903a3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"794265ee591b5b674b26e0e960492e85c681f4b012e0dd0cec89898d418903a3","first_computed_at":"2026-05-18T00:03:50.034898Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:03:50.034898Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IdkSwlh+P2BKyefXp5Fwaq6btqYHOwTAotw7N0eIdAd7D16UN9SA7HjpPdHq84ykr3NITaJ/1KyYzLx6p6GtCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:03:50.035381Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.08547","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ff00fbe2e3c911643e07c5a3d231cd30ec114b2b7ceeb478e57180c08f4eb3b8","sha256:1445c68cfb33244713fdcb0a161c6a30830911532a77649b743038c345d2f803"],"state_sha256":"c7b8908d00d8b10454898b65ee8b09ac204eaef87a2ef92832fc0488febd7147"}