{"paper":{"title":"When is hyponormality for 2-variable weighted shifts invariant under powers?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Jasang Yoon, Raul Curto","submitted_at":"2011-04-18T23:46:24Z","abstract_excerpt":"For 2-variable weighted shifts W_{(\\alpha,\\beta)}(T_1, T_2) we study the invariance of (joint) k- hyponormality under the action (h,\\ell) -> W_{(\\alpha,\\beta)}^{(h,\\ell)}(T_1, T_2):=(T_1^k,T_2^{\\ell}) (h,\\ell >=1). We show that for every k >= 1 there exists W_{(\\alpha,\\beta)}(T_1, T_2) such that W_{(\\alpha,\\beta)}^{(h,\\ell)}(T_1, T_2) is k-hyponormal (all h>=2,\\ell>=1) but W_{(\\alpha,\\beta)}(T_1, T_2) is not k-hyponormal. On the positive side, for a class of 2-variable weighted shifts with tensor core we find a computable necessary condition for invariance. Next, we exhibit a large nontrivial "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.3604","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"}