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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","authors_text":"Alvaro Arias, Jeff Farmer","cross_cats":[],"headline":"","license":"","primary_cat":"math.FA","submitted_at":"1994-02-08T00:00:00Z","title":"On the structure of tensor products of l_p spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9402205","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":"sha256:23ba5eedc0e768d916e1449ec2f7061c8f4128cd9e3c4375cee0469fe9425070","target":"record","created_at":"2026-05-18T01:05:51Z","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":"efccc5945599d9618c2dcae40a0760f73e621fe78a03fd684194f18d27bb303d","cross_cats_sorted":[],"license":"","primary_cat":"math.FA","submitted_at":"1994-02-08T00:00:00Z","title_canon_sha256":"2da333f8e668da0383e7885eec354d373761e7a0dff8223866bb4eabf3995847"},"schema_version":"1.0","source":{"id":"math/9402205","kind":"arxiv","version":1}},"canonical_sha256":"ece131bf8217060b7375582db4974789dda0aa6c90a58857a41dc0522930a464","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ece131bf8217060b7375582db4974789dda0aa6c90a58857a41dc0522930a464","first_computed_at":"2026-05-18T01:05:51.662618Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:51.662618Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"d69ngwqU0WwWZsAMT5zZtFpwhqJxXUkLOVzecHLIEA5KNTDuTXXDcS8bp/AmfwO1GXnyGXaGxEBUzYkvMPl0CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:51.663079Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9402205","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:23ba5eedc0e768d916e1449ec2f7061c8f4128cd9e3c4375cee0469fe9425070","sha256:76d574a0a5f559fb7c19fc8f2535a89ebaf0dd4c18beff2741af07b56df7910a"],"state_sha256":"a9fcb227fa247cebfebd626cc76735a99e2d35b51512c0a7545cdfb8f3f99670"}