{"paper":{"title":"Characterising weakly almost periodic functionals on the measure algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Matthew Daws","submitted_at":"2009-04-02T18:11:32Z","abstract_excerpt":"Let $G$ be a locally compact group, and consider the weakly-almost periodic functionals on $M(G)$, the measure algebra of $G$, denoted by $\\wap(M(G))$. This is a C$^*$-subalgebra of the commutative C$^*$-algebra $M(G)^*$, and so has character space, say $K_\\wap$. In this paper, we investigate properties of $K_\\wap$. We present a short proof that $K_\\wap$ can naturally be turned into a semigroup whose product is separately continuous: at the Banach algebra level, this product is simply the natural one induced by the Arens products. This is in complete agreement with the classical situation when"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0904.0436","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"}