{"paper":{"title":"On n-quasi left m-invertible operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"B. P. Duggal","submitted_at":"2018-12-01T15:59:12Z","abstract_excerpt":"A Hilbert space operator $S\\in\\B$ is $n$-quasi left $m$-invertible (resp., left $m$-invertible) by $T\\in\\B$, $m,n \\geq 1$ some integers, if $S^{*n}p(S,T)S^n=0$ (resp., $p(S,T)=0$), where $p(S,T)=\\sum_{j=0}^m{(-1)^{m-j}\\left(\\begin{array}{clcr}m\\\\j\\end{array}\\right)T^jS^j}$. Left $m$-invertible and $n$-quasi left $m$-invertible operators share a number of properties. Thus, if $S$ is $n$-quasi left $m$-invertible, then $S^n$ is the perturbation by a nilpotent of the direct sum of a left $m$-invertible with the $0$ operator. In particular, if $T=S^*$ (so that $S$ is $n$-quasi $m$-isomertric) and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.00221","kind":"arxiv","version":6},"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"}