{"paper":{"title":"Power bounded $m$-left invertible operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"B.P. Duggal, C.S. Kubrusly","submitted_at":"2019-03-08T13:17:27Z","abstract_excerpt":"A Hilbert space operator $S\\in\\B$ is left $m$-invertible by $T\\in\\B$ if $$\\sum_{j=0}^m{(-1)^{m-j}\\left(\\begin{array}{clcr}m\\\\j\\end{array}\\right)T^jS^j}=0,$$ $S$ is $m$-isometric if $$\\sum_{j=0}^m{(-1)^{m-j}\\left(\\begin{array}{clcr}m\\\\j\\end{array}\\right){S^*}^jS^j}=0$$ and $S$ is $(m,C)$-isometric for some conjugation $C$ of $\\H$ if $$\\sum_{j=0}^m{(-1)^{m-j}\\left(\\begin{array}{clcr}m\\\\j\\end{array}\\right){S^*}^jCS^jC}=0.$$ If a power bounded operator $S$ is left invertible by a power bounded operator $T$, then $S$ (also, $T^*$) is similar to an isometry. Translated to $m$-isometric and $(m,C)$-i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.03417","kind":"arxiv","version":2},"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"}