{"paper":{"title":"Averages over matrix unitary orbits and spectral order","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Eun-Young Lee, Jean-Christophe Bourin","submitted_at":"2026-06-14T06:21:15Z","abstract_excerpt":"We establish matrix versions of the comparisons between the $\\ell^p$-norms or quasi-norms for sequences of complex numbers. For instance, given $1\\ge q>0$, and a family of $m$ normal $d\\times d$ matrices $A_1,\\ldots, A_m$, we show that $$ \\left|\\sum_{k=1}^m A_k\\right| \\le \\frac{1}{d}\\sum_{i=1}^d V_i\\left\\{\\sum_{k=1}^m |A_k|^{q}\\right\\}^{1/q}\\!\\!\\!\\!V_i^* $$ for some unitary $d\\times d$ matrices $V_1,\\ldots, V_d$. We also give applications to Olson's spectral order and to the comparison between the symmetric modulus and the quadratic symmetric modulus. In particular we show that the sum $A+B$ o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.15624","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.15624/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}