{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:B7VFIEF3A6UCIEFGJLCQJYCN37","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":"3497af10ee9a1937a71b298c36cc0b7a3394908b083536b817510d546480f5b1","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-10-29T17:06:59Z","title_canon_sha256":"bbcd8b26cb2fe3b569d4162c0057123c1530b74dae688fce913ca54bc0dc6014"},"schema_version":"1.0","source":{"id":"1310.7880","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.7880","created_at":"2026-05-18T03:08:27Z"},{"alias_kind":"arxiv_version","alias_value":"1310.7880v1","created_at":"2026-05-18T03:08:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.7880","created_at":"2026-05-18T03:08:27Z"},{"alias_kind":"pith_short_12","alias_value":"B7VFIEF3A6UC","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"B7VFIEF3A6UCIEFG","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"B7VFIEF3","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:4d55f99417573435c66509d78439096e55fa428e13bf21746a377dea49c83f2b","target":"graph","created_at":"2026-05-18T03:08:27Z","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":"Let $(M_i)_{i}$ be a (finite or infinite) family of finite von Neumann algebras with a common subalgebra $P$. When $\\varphi:\\IN\\rightarrow\\IC$ is a function, we define the radial multiplier $M_\\varphi$ on the amalgamated free product $M=M_1\\free_P M_2\\free_P\\ldots$ setting $M_{\\varphi}(x)=\\varphi(n)x$ for every reduced expression $x$ of length $n$. In this paper we give a sufficient condition on $\\varphi$ to ensure that the corresponding radial multiplier $M_\\varphi$ is a completely bounded map, and moreover we give an upper bound on its completely bounded norm. Our condition on $\\varphi$ does","authors_text":"Steven Deprez","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-10-29T17:06:59Z","title":"Radial multipliers on arbitrary amalgamated free products of finite von Neumann algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.7880","kind":"arxiv","version":1},"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":"sha256:572229732b1285d656e647f78eb501556cd8080b26c40abca0e65a3b89428d2a","target":"record","created_at":"2026-05-18T03:08:27Z","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":"3497af10ee9a1937a71b298c36cc0b7a3394908b083536b817510d546480f5b1","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-10-29T17:06:59Z","title_canon_sha256":"bbcd8b26cb2fe3b569d4162c0057123c1530b74dae688fce913ca54bc0dc6014"},"schema_version":"1.0","source":{"id":"1310.7880","kind":"arxiv","version":1}},"canonical_sha256":"0fea5410bb07a82410a64ac504e04ddfe8c486c23d658c492efe0617ef8d241a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0fea5410bb07a82410a64ac504e04ddfe8c486c23d658c492efe0617ef8d241a","first_computed_at":"2026-05-18T03:08:27.741513Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:08:27.741513Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"s4y9HHYJjxugbxTRk6qZBAbvAY88y+34pb7HDl31cv+f01390wPmol7elwtSBRL88tgKuL83qhiLehyMr4ObDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:08:27.742198Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.7880","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:572229732b1285d656e647f78eb501556cd8080b26c40abca0e65a3b89428d2a","sha256:4d55f99417573435c66509d78439096e55fa428e13bf21746a377dea49c83f2b"],"state_sha256":"3b8be02b7cc59214b9ebcd32e01524acc5ac2c857b12cfeb6684a22dfe6d30f0"}