{"paper":{"title":"$N$-hypercontractivity and similarity of Cowen-Douglas operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Hyun-Kyoung Kwon, Jing Xu, Kui Ji","submitted_at":"2019-01-28T00:33:40Z","abstract_excerpt":"When the backward shift operator on a weighted space $H^2_w=\\{f=\\sum_{j=0} ^{\\infty} a_jz^j : \\sum_{j=0}^{\\infty} |a_j|^2w_j < \\infty\\}$ is an $n$-hypercontraction, we prove that the weights must satisfy the inequality $$\\frac{w_{j+1}}{w_j} \\leq {\\frac{1+j}{n+j}}.$$ As an application of this result, it is shown that such an operator cannot be subnormal. We also give an example to illustrate the important role that the $n$-hypercontractivity assumption plays in determining the similarity of Cowen-Douglas operators in terms of the curvatures of their eigenvector bundles."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.09471","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"}