{"paper":{"title":"Weak null maximum and integration of families of multiplication operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.FA","authors_text":"David Norrbo","submitted_at":"2025-09-05T15:17:24Z","abstract_excerpt":"Let $X$ be a reflexive Hardy space or weighted Bergman space on the unit disk in the complex plane. For a bounded linear operator $S$ on $X$, let $\\textrm{wem}(S):= \\sup_{(f_n)} \\limsup_n \\|Sf_n\\|$, that is, the supremum of cluster points of $n\\mapsto \\|S f_n\\|$, where $(f_n)$ is any unit norm weakly null sequence. This quantity coincides with the essential norm on the reflexive weighted Bergman spaces.\n  For a suitable family $\\{ g_t : t\\in]0,1[ \\}$ of bounded analytic functions on the unit disk, we characterize when one can exchange $\\textrm{wem}(\\cdot)$ and integration over $t$ of the multi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.05173","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2509.05173/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"}