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We combine these results with combinatorial arguments to address the question of primarity for these spaces and their duals.\n  Our main results are: \\medbreak \\item{(1)} If $1<p<\\infty$, then $B(\\ell_p)\\approx B(L_p)$ ($B(X)$ consists of the bounded linear operators on $X$). \\medbreak \\item{(2)} If ${1\\over p_i}+{1\\over p_j}\\leq1$ for every $i\\neq j$, or if all of the $p_i$'s are equal, then $\\ell_{p_1}\\hat{\\otimes}\\cdots"},"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":"math/9402205","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.FA","submitted_at":"1994-02-08T00:00:00Z","cross_cats_sorted":[],"title_canon_sha256":"2da333f8e668da0383e7885eec354d373761e7a0dff8223866bb4eabf3995847","abstract_canon_sha256":"efccc5945599d9618c2dcae40a0760f73e621fe78a03fd684194f18d27bb303d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:51.663079Z","signature_b64":"d69ngwqU0WwWZsAMT5zZtFpwhqJxXUkLOVzecHLIEA5KNTDuTXXDcS8bp/AmfwO1GXnyGXaGxEBUzYkvMPl0CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ece131bf8217060b7375582db4974789dda0aa6c90a58857a41dc0522930a464","last_reissued_at":"2026-05-18T01:05:51.662618Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:51.662618Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the structure of tensor products of l_p spaces","license":"","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Alvaro Arias, Jeff Farmer","submitted_at":"1994-02-08T00:00:00Z","abstract_excerpt":"We examine some structural properties of (injective and projective) tensor products of $\\ell_p$-spaces (projections, complemented subspaces, reflexivity, isomorphisms, etc.). We combine these results with combinatorial arguments to address the question of primarity for these spaces and their duals.\n  Our main results are: \\medbreak \\item{(1)} If $1<p<\\infty$, then $B(\\ell_p)\\approx B(L_p)$ ($B(X)$ consists of the bounded linear operators on $X$). \\medbreak \\item{(2)} If ${1\\over p_i}+{1\\over p_j}\\leq1$ for every $i\\neq j$, or if all of the $p_i$'s are equal, then $\\ell_{p_1}\\hat{\\otimes}\\cdots"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9402205","kind":"arxiv","version":1},"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":"math/9402205","created_at":"2026-05-18T01:05:51.662689+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/9402205v1","created_at":"2026-05-18T01:05:51.662689+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9402205","created_at":"2026-05-18T01:05:51.662689+00:00"},{"alias_kind":"pith_short_12","alias_value":"5TQTDP4CC4DA","created_at":"2026-05-18T12:25:47.102015+00:00"},{"alias_kind":"pith_short_16","alias_value":"5TQTDP4CC4DAW43V","created_at":"2026-05-18T12:25:47.102015+00:00"},{"alias_kind":"pith_short_8","alias_value":"5TQTDP4C","created_at":"2026-05-18T12:25:47.102015+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/5TQTDP4CC4DAW43VLAW3JF2HRH","json":"https://pith.science/pith/5TQTDP4CC4DAW43VLAW3JF2HRH.json","graph_json":"https://pith.science/api/pith-number/5TQTDP4CC4DAW43VLAW3JF2HRH/graph.json","events_json":"https://pith.science/api/pith-number/5TQTDP4CC4DAW43VLAW3JF2HRH/events.json","paper":"https://pith.science/paper/5TQTDP4C"},"agent_actions":{"view_html":"https://pith.science/pith/5TQTDP4CC4DAW43VLAW3JF2HRH","download_json":"https://pith.science/pith/5TQTDP4CC4DAW43VLAW3JF2HRH.json","view_paper":"https://pith.science/paper/5TQTDP4C","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/9402205&json=true","fetch_graph":"https://pith.science/api/pith-number/5TQTDP4CC4DAW43VLAW3JF2HRH/graph.json","fetch_events":"https://pith.science/api/pith-number/5TQTDP4CC4DAW43VLAW3JF2HRH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5TQTDP4CC4DAW43VLAW3JF2HRH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5TQTDP4CC4DAW43VLAW3JF2HRH/action/storage_attestation","attest_author":"https://pith.science/pith/5TQTDP4CC4DAW43VLAW3JF2HRH/action/author_attestation","sign_citation":"https://pith.science/pith/5TQTDP4CC4DAW43VLAW3JF2HRH/action/citation_signature","submit_replication":"https://pith.science/pith/5TQTDP4CC4DAW43VLAW3JF2HRH/action/replication_record"}},"created_at":"2026-05-18T01:05:51.662689+00:00","updated_at":"2026-05-18T01:05:51.662689+00:00"}