{"paper":{"title":"Strictly singular operators in Tsirelson like spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Kevin Beanland, Pavlos Motakis, Spiros Argyros","submitted_at":"2013-09-18T01:35:46Z","abstract_excerpt":"For each $n \\in \\mathbb{N}$ a Banach space $\\mathfrak{X}_{0,1}^n$ is constructed is having the property that every normalized weakly null sequence generates either a $c_0$ or $\\ell_1$ spreading models and every infinite dimensional subspace has weakly null sequences generating both $c_0$ and $\\ell_1$ spreading models. The space $\\mathfrak{X}_{0,1}^n$ is also quasiminimal and for every infinite dimensional closed subspace $Y$ of $\\mathfrak{X}_{0,1}^n$, for every $S_1,S_2,\\ldots,S_{n+1}$ strictly singular operators on $Y$, the operator $S_1S_2\\cdots S_{n+1}$ is compact. Moreover, for every subsp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.4516","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"}