{"paper":{"title":"Bounded linear operators between C^*-algebras","license":"","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Gilles Pisier, U. Haagerup","submitted_at":"1993-02-18T19:43:15Z","abstract_excerpt":"Let $u:A\\to B$ be a bounded linear operator between two $C^*$-algebras $A,B$. The following result was proved by the second author.\n  Theorem 0.1. There is a numerical constant $K_1$ such that for all finite sequences $x_1,\\ldots, x_n$ in $A$ we have $$\\leqalignno{&\\max\\left\\{\\left\\|\\left(\\sum u(x_i)^* u(x_i)\\right)^{1/2}\\right\\|_B, \\left\\|\\left(\\sum u(x_i) u(x_i)^*\\right)^{1/2}\\right\\|_B\\right\\}&(0.1)_1\\cr \\le &K_1\\|u\\| \\max\\left\\{\\left\\|\\left(\\sum x^*_ix_i\\right)^{1/2}\\right\\|_A, \\left\\|\\left(\\sum x_ix^*_i\\right)^{1/2}\\right\\|_A\\right\\}.}$$\n  A simpler proof was given in [H1]. More recently "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9302214","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"}