{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:AJB6S3W4GYV6CU2VVH22L57TDS","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":"1d2fc58a6d4c09b7fa83739584c4229dd9d8cb4801a03b04e523f749affc7268","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-07-02T20:15:30Z","title_canon_sha256":"6a613a3b6f56c82da8c848325e2f6aa6e25df2bf50b93cbe742b8fed61be2d24"},"schema_version":"1.0","source":{"id":"1807.00875","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.00875","created_at":"2026-05-18T00:10:09Z"},{"alias_kind":"arxiv_version","alias_value":"1807.00875v2","created_at":"2026-05-18T00:10:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.00875","created_at":"2026-05-18T00:10:09Z"},{"alias_kind":"pith_short_12","alias_value":"AJB6S3W4GYV6","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"AJB6S3W4GYV6CU2V","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"AJB6S3W4","created_at":"2026-05-18T12:32:13Z"}],"graph_snapshots":[{"event_id":"sha256:9a82884b42e54c0dd2e12ed1bde915010934db7a144acadec24ddeca5f7a93ba","target":"graph","created_at":"2026-05-18T00:10:09Z","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 show that the analyticity of semigroups $(T_t)_{t \\geq 0}$ of (not necessarily positive) selfadjoint contractive Fourier multipliers on $\\mathrm{L}^p$-spaces of any abelian locally compact group is preserved by the tensorisation of the identity operator $\\mathrm{Id}_X$ of a Banach space $X$ for a large class of K-convex Banach spaces, answering partially a conjecture of Pisier. The result is even new for semigroups of Fourier multipliers acting on $\\mathrm{L}^p(\\mathbb{R}^n)$. The proof relies on the use of noncommutative Banach spaces and we give a more general result for semigroups of Fou","authors_text":"C\\'edric Arhancet","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-07-02T20:15:30Z","title":"On analyticity of semigroups on Bochner spaces and on vector-valued noncommutative $\\mathrm{L}^p$-spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.00875","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":"sha256:99ce715514220a878b0033346e95cbe57a99e3dd8f49fbe78db262f9a8fc6607","target":"record","created_at":"2026-05-18T00:10:09Z","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":"1d2fc58a6d4c09b7fa83739584c4229dd9d8cb4801a03b04e523f749affc7268","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-07-02T20:15:30Z","title_canon_sha256":"6a613a3b6f56c82da8c848325e2f6aa6e25df2bf50b93cbe742b8fed61be2d24"},"schema_version":"1.0","source":{"id":"1807.00875","kind":"arxiv","version":2}},"canonical_sha256":"0243e96edc362be15355a9f5a5f7f31cb4eecc51336b24b8b7fd40ca2ed70747","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0243e96edc362be15355a9f5a5f7f31cb4eecc51336b24b8b7fd40ca2ed70747","first_computed_at":"2026-05-18T00:10:09.912702Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:10:09.912702Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3wpITSqjbEa68azM/N6Ga2LGUP8mBZWwgsTzAMyJKiQ8nbFaQ3X94zMrn5xeG1TkTzJWKtM1SSu+SCQtG36yAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:10:09.913280Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.00875","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:99ce715514220a878b0033346e95cbe57a99e3dd8f49fbe78db262f9a8fc6607","sha256:9a82884b42e54c0dd2e12ed1bde915010934db7a144acadec24ddeca5f7a93ba"],"state_sha256":"5a8fc67d8cecc08d0122aed279635ed3a0dde005661a97e0a901047a2faf7055"}