{"paper":{"title":"Spaces of operator-valued functions measurable with respect to the strong operator topology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Jan van Neerven, Oscar Blasco","submitted_at":"2008-11-14T12:06:46Z","abstract_excerpt":"Let $X$ and $Y$ be Banach spaces and $(\\Omega,\\Sigma,\\mu)$ a finite measure space. In this note we introduce the space $L^p[\\mu;L(X,Y)]$ consisting of all (equivalence classes of) functions $\\Phi:\\Omega \\mapsto L(X,Y)$ such that $\\omega \\mapsto \\Phi(\\omega)x$ is strongly $\\mu$-measurable for all $x\\in X$ and $\\omega \\mapsto \\Phi(\\omega)f(\\omega)$ belongs to $L^1(\\mu;Y)$ for all $f\\in L^{p'}(\\mu;X)$, $1/p+1/p'=1$. We show that functions in $L^p[\\mu;\\L(X,Y)]$ define operator-valued measures with bounded $p$-variation and use these spaces to obtain an isometric characterization of the space of al"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0811.2284","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/0811.2284/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"}