{"paper":{"title":"On strictly singular operators between separable Banach spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Kevin Beanland, Pandelis Dodos","submitted_at":"2010-06-14T11:18:07Z","abstract_excerpt":"Let $X$ and $Y$ be separable Banach spaces and denote by $\\sss\\sss(X,Y)$ the subset of $\\llll(X,Y)$ consisting of all strictly singular operators. We study various ordinal ranks on the set $\\sss\\sss(X,Y)$. Our main results are summarized as follows. Firstly, we define a new rank $\\rs$ on $\\sss\\sss(X,Y)$. We show that $\\rs$ is a co-analytic rank and that dominates the rank $\\varrho$ introduced by Androulakis, Dodos, Sirotkin and Troitsky [Israel J. Math., 169 (2009), 221-250]. Secondly, for every $1\\leq p<+\\infty$ we construct a Banach space $Y_p$ with an unconditional basis such that $\\sss\\sss"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.2672","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"}