{"paper":{"title":"Comparing gaussian and Rademacher cotype for operators on the space of continous functions","license":"","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Marius Junge","submitted_at":"1993-02-04T19:45:37Z","abstract_excerpt":"We will prove an abstract comparision principle which translates gaussian cotype in Rademacher cotype conditions and vice versa. More precisely, let $2\\!<\\!q\\!<\\!\\infty$ and $T:\\,C(K)\\,\\to\\,F$ a linear, continous operator.\n  T is of gaussian cotype q if and only if\n  ( \\summ_1^n (\\frac{|| Tx_k||_F}{\\sqrt{\\log(k+1)}})^q )^{1/q} \\, \\le c || \\summ_1^n \\varepsilon_k x_k ||_{L_2(C(K))} ,\n  for all sequences with $(|| Tx_k ||)_1^n$ decreasing.\n  T is of Rademacher cotype q if and only if\n  (\\summ_1^n (|| Tx_k||_F \\,\\sqrt{\\log(k+1)})^q )^{1/q} \\, \\le c || \\summ_1^n g_k x_k ||_{L_2(C(K))} ,\n  for all "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9302206","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"}