{"paper":{"title":"The ascent and descent of weighted conditional expectation operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Yousef Estaremi","submitted_at":"2017-11-05T06:35:34Z","abstract_excerpt":"In this paper we prove that the ascent of a weighted conditional expectation operator of the form of $M_wEM_u$ on $L^p$-spaces is always finite and is equal to 2. Also we get that under a weak condition the descent of $M_wEM_u$ is finite and is equal to 2 too. Moreover, we give some necessary and sufficient conditions for $M_wE M_u$ to be power bounded. In the sequel we apply some results in operator theory on ascent and descent to $M_wEM_u$. Finally we find that $T=M_wEM_u$ is Cesaro bounded if and only if $\\widehat{T}$ is Cesaro bounded."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.01540","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"}