{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:AJB6S3W4GYV6CU2VVH22L57TDS","short_pith_number":"pith:AJB6S3W4","schema_version":"1.0","canonical_sha256":"0243e96edc362be15355a9f5a5f7f31cb4eecc51336b24b8b7fd40ca2ed70747","source":{"kind":"arxiv","id":"1807.00875","version":2},"attestation_state":"computed","paper":{"title":"On analyticity of semigroups on Bochner spaces and on vector-valued noncommutative $\\mathrm{L}^p$-spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"C\\'edric Arhancet","submitted_at":"2018-07-02T20:15:30Z","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1807.00875","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-07-02T20:15:30Z","cross_cats_sorted":[],"title_canon_sha256":"6a613a3b6f56c82da8c848325e2f6aa6e25df2bf50b93cbe742b8fed61be2d24","abstract_canon_sha256":"1d2fc58a6d4c09b7fa83739584c4229dd9d8cb4801a03b04e523f749affc7268"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:10:09.913280Z","signature_b64":"3wpITSqjbEa68azM/N6Ga2LGUP8mBZWwgsTzAMyJKiQ8nbFaQ3X94zMrn5xeG1TkTzJWKtM1SSu+SCQtG36yAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0243e96edc362be15355a9f5a5f7f31cb4eecc51336b24b8b7fd40ca2ed70747","last_reissued_at":"2026-05-18T00:10:09.912702Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:10:09.912702Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On analyticity of semigroups on Bochner spaces and on vector-valued noncommutative $\\mathrm{L}^p$-spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"C\\'edric Arhancet","submitted_at":"2018-07-02T20:15:30Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.00875","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1807.00875","created_at":"2026-05-18T00:10:09.912782+00:00"},{"alias_kind":"arxiv_version","alias_value":"1807.00875v2","created_at":"2026-05-18T00:10:09.912782+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.00875","created_at":"2026-05-18T00:10:09.912782+00:00"},{"alias_kind":"pith_short_12","alias_value":"AJB6S3W4GYV6","created_at":"2026-05-18T12:32:13.499390+00:00"},{"alias_kind":"pith_short_16","alias_value":"AJB6S3W4GYV6CU2V","created_at":"2026-05-18T12:32:13.499390+00:00"},{"alias_kind":"pith_short_8","alias_value":"AJB6S3W4","created_at":"2026-05-18T12:32:13.499390+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/AJB6S3W4GYV6CU2VVH22L57TDS","json":"https://pith.science/pith/AJB6S3W4GYV6CU2VVH22L57TDS.json","graph_json":"https://pith.science/api/pith-number/AJB6S3W4GYV6CU2VVH22L57TDS/graph.json","events_json":"https://pith.science/api/pith-number/AJB6S3W4GYV6CU2VVH22L57TDS/events.json","paper":"https://pith.science/paper/AJB6S3W4"},"agent_actions":{"view_html":"https://pith.science/pith/AJB6S3W4GYV6CU2VVH22L57TDS","download_json":"https://pith.science/pith/AJB6S3W4GYV6CU2VVH22L57TDS.json","view_paper":"https://pith.science/paper/AJB6S3W4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1807.00875&json=true","fetch_graph":"https://pith.science/api/pith-number/AJB6S3W4GYV6CU2VVH22L57TDS/graph.json","fetch_events":"https://pith.science/api/pith-number/AJB6S3W4GYV6CU2VVH22L57TDS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AJB6S3W4GYV6CU2VVH22L57TDS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AJB6S3W4GYV6CU2VVH22L57TDS/action/storage_attestation","attest_author":"https://pith.science/pith/AJB6S3W4GYV6CU2VVH22L57TDS/action/author_attestation","sign_citation":"https://pith.science/pith/AJB6S3W4GYV6CU2VVH22L57TDS/action/citation_signature","submit_replication":"https://pith.science/pith/AJB6S3W4GYV6CU2VVH22L57TDS/action/replication_record"}},"created_at":"2026-05-18T00:10:09.912782+00:00","updated_at":"2026-05-18T00:10:09.912782+00:00"}