{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:RBNGSLU6WCV45PEKNOMJXFAZ3U","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":"431ad896a082bccdaadd074403f61458403e698c6330c1211cfdd672726c98da","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-01-23T15:38:35Z","title_canon_sha256":"01474215d95c67181d2185e40db56a980a471c42437b61f0233d102ff4b1d99e"},"schema_version":"1.0","source":{"id":"1501.05834","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.05834","created_at":"2026-05-18T02:19:35Z"},{"alias_kind":"arxiv_version","alias_value":"1501.05834v2","created_at":"2026-05-18T02:19:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.05834","created_at":"2026-05-18T02:19:35Z"},{"alias_kind":"pith_short_12","alias_value":"RBNGSLU6WCV4","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"RBNGSLU6WCV45PEK","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"RBNGSLU6","created_at":"2026-05-18T12:29:39Z"}],"graph_snapshots":[{"event_id":"sha256:eb79bd1010b9cd6e6517695dc02929ee05d50feb1c0b294bfc1c883a380d892b","target":"graph","created_at":"2026-05-18T02:19:35Z","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 consider a bounded linear operator $T$ on a complex Banach space $X$ and show that its spectral radius $r(T)$ satisfies $r(T) < 1$ if all sequences $(< x',T^nx>)_{n \\in \\mathbb{N}_0}$ ($x \\in X$, $x' \\in X'$) are, up to a certain rearrangement, contained in a principal ideal of the space $c_0$ of sequences which converge to $0$. From this result we obtain generalizations of theorems of G. Weiss and J. van Neerven. We also prove a related result on $C_0$-semigroups.","authors_text":"Jochen Gl\\\"uck","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-01-23T15:38:35Z","title":"On Weak Decay Rates and Uniform Stability of Bounded Linear Operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.05834","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":"sha256:0b141e92b6f84a95c5b621d8e8821826a16f8fc3bcc2a2a57dc02bf2d8f345ab","target":"record","created_at":"2026-05-18T02:19:35Z","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":"431ad896a082bccdaadd074403f61458403e698c6330c1211cfdd672726c98da","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-01-23T15:38:35Z","title_canon_sha256":"01474215d95c67181d2185e40db56a980a471c42437b61f0233d102ff4b1d99e"},"schema_version":"1.0","source":{"id":"1501.05834","kind":"arxiv","version":2}},"canonical_sha256":"885a692e9eb0abcebc8a6b989b9419dd1810a45d44c34df8960318e3cc7c481a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"885a692e9eb0abcebc8a6b989b9419dd1810a45d44c34df8960318e3cc7c481a","first_computed_at":"2026-05-18T02:19:35.674347Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:19:35.674347Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/iyIxZo5pORpXOpf6I8LIiraZkNWtNK6eOywVVIUL7sLq3qY7r7beR2/2QkB1H0P+s+nMbN09UXYikZAK0SBBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:19:35.674774Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.05834","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0b141e92b6f84a95c5b621d8e8821826a16f8fc3bcc2a2a57dc02bf2d8f345ab","sha256:eb79bd1010b9cd6e6517695dc02929ee05d50feb1c0b294bfc1c883a380d892b"],"state_sha256":"dbaae91cec26ee900c44e5adaa849b194029c13d0fb5d156e464d176591692f1"}