{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:5HEQGDLS6RTORFFWR2LRUAQHDA","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":"51cafbfb7a873e0f367553c5b6157c4041470d0b550d88752005af082c935f02","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-07-02T11:36:47Z","title_canon_sha256":"5499094fa339e7b6ebc4a1194256c8175f473f39e02164075d414176332ba770"},"schema_version":"1.0","source":{"id":"1407.0525","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.0525","created_at":"2026-05-18T01:17:53Z"},{"alias_kind":"arxiv_version","alias_value":"1407.0525v2","created_at":"2026-05-18T01:17:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.0525","created_at":"2026-05-18T01:17:53Z"},{"alias_kind":"pith_short_12","alias_value":"5HEQGDLS6RTO","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"5HEQGDLS6RTORFFW","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"5HEQGDLS","created_at":"2026-05-18T12:28:14Z"}],"graph_snapshots":[{"event_id":"sha256:75ae68b0a803ea68bd55a25ac279138246269c501722625f8a0265ba20561694","target":"graph","created_at":"2026-05-18T01:17:53Z","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":"Sz.-Nagy's famous theorem states that a bounded operator $T$ which acts on a complex Hilbert space $\\mathcal{H}$ is similar to a unitary operator if and only if $T$ is invertible and both $T$ and $T^{-1}$ are power bounded. There is an equivalent reformulation of that result which considers the self-adjoint iterates of $T$ and uses a Banach limit $L$. In this paper first we present a generalization of the necessity part in Sz.-Nagy's result concerning operators that are similar to normal operators. In the second part we provide characterization of all possible strong operator topology limits o","authors_text":"Gy\\\"orgy P\\'al Geh\\'er","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-07-02T11:36:47Z","title":"Asymptotic limits of operators similar to normal operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.0525","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:c60b453b26e24e08c3375779c5e701b430f1f8cce252042bc6b8b61db618ebe0","target":"record","created_at":"2026-05-18T01:17:53Z","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":"51cafbfb7a873e0f367553c5b6157c4041470d0b550d88752005af082c935f02","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-07-02T11:36:47Z","title_canon_sha256":"5499094fa339e7b6ebc4a1194256c8175f473f39e02164075d414176332ba770"},"schema_version":"1.0","source":{"id":"1407.0525","kind":"arxiv","version":2}},"canonical_sha256":"e9c9030d72f466e894b68e971a02071805b1e3a69faf713c81776dbc4fe9445f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e9c9030d72f466e894b68e971a02071805b1e3a69faf713c81776dbc4fe9445f","first_computed_at":"2026-05-18T01:17:53.320482Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:17:53.320482Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YIlIjZ9D7oTC/iomsQuQ2mvHeXfoYePLrO5STj6m3zOibe7JhpkH43RpfJnS0HJrBVOOFUoSGGwTr4+EyQxFDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:17:53.321206Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.0525","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c60b453b26e24e08c3375779c5e701b430f1f8cce252042bc6b8b61db618ebe0","sha256:75ae68b0a803ea68bd55a25ac279138246269c501722625f8a0265ba20561694"],"state_sha256":"3e77aaa68e2688d7733b46b129c0220e6164963b3aa59c6f9fe3a9064f231590"}