{"paper":{"title":"Bloch-type spaces and extended Ces\\`{a}ro operators in the unit ball of a complex Banach space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Hidetaka Hamada","submitted_at":"2017-10-31T06:55:22Z","abstract_excerpt":"Let $\\mathbb{B}$ be the unit ball of a complex Banach space $X$. In this paper, we will generalize the Bloch-type spaces and the little Bloch-type spaces to the open unit ball $\\mathbb{B}$ by using the radial derivative. Next, we define an extended Ces\\`{a}ro operator $T_{\\varphi}$ with holomorphic symbol $\\varphi$ and characterize those $\\varphi$ for which $T_{\\varphi}$ is bounded between the Bloch-type spaces and the little Bloch-type spaces. We also characterize those $\\varphi$ for which $T_{\\varphi}$ is compact between the Bloch-type spaces and the little Bloch-type spaces under some addit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.11347","kind":"arxiv","version":3},"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"}