{"paper":{"title":"Strict singularity of a Volterra-type integral operator on $H^p$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Santeri Miihkinen","submitted_at":"2015-09-28T15:23:15Z","abstract_excerpt":"We prove that a Volterra-type integral operator $T_gf(z) = \\int_0^z f(\\zeta)g'(\\zeta)d\\zeta, \\, z \\in \\mathbb D,$ defined on Hardy spaces $H^p, \\, 1 \\le p < \\infty,$ fixes an isomorphic copy of $\\ell^p,$ if the operator $T_g$ is not compact. In particular, this shows that the strict singularity of the operator $T_g$ coincides with the compactness of the operator $T_g$ on spaces $H^p.$ As a consequence, we obtain a new proof for the equivalence of the compactness and the weak compactness of the operator $T_g$ on $H^1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.08356","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"}