{"paper":{"title":"On the second parameter of an $(m, p)$-isometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Michael Mackey, M\\'iche\\'al \\'O Searc\\'oid, Philipp Hoffmann","submitted_at":"2011-06-01T23:29:02Z","abstract_excerpt":"A bounded linear operator $T$ on a Banach space $X$ is called an $(m, p)$-isometry if it satisfies the equation \\sum_{k=0}^{m}(-1)^{k} {m \\choose k}\\|T^{k}x\\|^{p} = 0$, for all $x \\in X$. In this paper we study the structure which underlies the second parameter of $(m, p)$-isometric operators. We concentrate on determining when an $(m, p)$-isometry is a $(\\mu, q)$-isometry for some pair ($\\mu, q)$. We also extend the definition of $(m, p)$-isometry, to include $p=\\infty$ and study basic properties of these $(m, \\infty)$-isometries."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.0339","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"}