{"paper":{"title":"Norms of idempotent Schur multipliers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Rupert H. Levene","submitted_at":"2013-02-20T09:39:45Z","abstract_excerpt":"Let D be a masa in B(H) where H is a separable Hilbert space. We find real numbers \\eta_0 < \\eta_1 < \\eta_2 < ... < \\eta_6 so that for every bounded, normal D-bimodule map {\\Phi} on B(H) either ||\\Phi|| > \\eta_6, or ||\\Phi|| = \\eta_k for some k <= 6. When D is totally atomic, these maps are the idempotent Schur multipliers and we characterise those with norm \\eta_k for 0 <= k <= 6. We also show that the Schur idempotents which keep only the diagonal and superdiagonal of an n x n matrix, or of an n x (n+1) matrix, both have norm 2/(n+1) cot(pi/(n+1)), and we consider the average norm of a rando"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.4849","kind":"arxiv","version":2},"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"}