{"paper":{"title":"On $(n,k)$-quasi-*-paranormal operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Huaijie Zhong, Qingping Zeng","submitted_at":"2012-09-23T11:13:09Z","abstract_excerpt":"For nonnegative integers $n$ and $k$, we introduce in this paper a new class of $(n,k)$-quasi-*-paranormal operators satisfying\n  $$||T^{1+n}(T^{k}x)||^{1/(1+n)}||T^{k}x||^{n/(1+n)} \\geq\n  ||T^*(T^{k}x)|| \\makebox{\\ for all} x \\in H.$$\n  This class includes the class of $n$-*-paranormal operators and the class of $(1,k)$-quasi-*-paranormal operators contains the class of $k$-quasi-*-class $A$ operators. We study basic properties of $(n,k)$-quasi-*-paranormal operators: (1) inclusion relations and examples; (2) a matrix representation; (3) joint (approximate) point spectrum and single valued ex"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.5050","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"}