{"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"}