{"paper":{"title":"Structural rigidity of generalised Volterra operators on $H^p$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Eero Saksman, Hans-Olav Tylli, Pekka J. Nieminen, Santeri Miihkinen","submitted_at":"2017-10-03T16:17:00Z","abstract_excerpt":"We show that the non-compact generalised analytic Volterra operators $T_g$, where $g \\in \\mathit{BMOA}$, have the following structural rigidity property on the Hardy spaces $H^p$ for $1 \\le p < \\infty$ and $p \\neq 2$: if $T_g$ is bounded below on an infinite-dimensional subspace $M \\subset H^p$, then $M$ contains a subspace linearly isomorphic to $\\ell^p$. This implies in particular that any Volterra operator $T_g\\colon H^p \\to H^p$ is $\\ell^2$-singular for $p \\neq 2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.01252","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"}