{"paper":{"title":"On subspaces of invariant vectors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.RT"],"primary_cat":"math.GR","authors_text":"Tatiana Shulman","submitted_at":"2015-09-17T14:04:21Z","abstract_excerpt":"Let $X_{\\pi}$ be the subspace of fixed vectors for a uniformly bounded representation $\\pi$ of a group $G$ on a Banach space $X$. We study the problem of the existence and uniqueness of a subspace $Y$ that complements $X_{\\pi}$ in $X$. Similar questions for $G$-invariant complement to $X_{\\pi}$ are considered. We prove that every non-amenable discrete group $G$ has a representation with non-complemented $X_{\\pi}$ and find some conditions that provide an $G$-invariant complement. A special attention is given to representations on $C(K)$ that arise from an action of $G$ on a metric compact $K$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.05263","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"}