{"paper":{"title":"Isometries of Hilbert space valued function spaces","license":"","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Beata Randrianantoanina","submitted_at":"1994-11-16T22:08:45Z","abstract_excerpt":"Let $X$ be a (real or complex) rearrangement-in\\-va\\-riant function space on $\\Om$ (where $\\Om = [0,1]$ or $\\Om \\subseteq \\bbN$) whose norm is not proportional to the $L_2$-norm. Let $H$ be a separable Hilbert space. We characterize surjective isometries of $X(H).$ We prove that if $T$ is such an isometry then there exist Borel maps $a:\\Om\\to\\bbK$ and $\\sigma:\\Om\\lra\\Om$ and a strongly measurable operator map $S$ of $\\Om$ into $\\calB(H)$ so that for almost all $\\om$ $S(\\om)$ is a surjective isometry of $H$\n  and for any $f\\in X(H)$ $$Tf(\\om)=a(\\om)S(\\om)(f(\\sigma(\\om))) \\text{ a.e.}$$\n  As a c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9411210","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"}