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We characterize the norm one idempotents in $M_{cb}A(G)$: the indicator function of a set $E \\subset G$ is a norm one idempotent in $M_{cb}A(G)$ if and only if $E$ is a coset of an open subgroup of $G$. As applications, we describe the closed ideals of $A_{Mcb}(G)$ with an approximate identity bounded by 1, and we characterize those $G$ for which $A_{Mcb}(G)$ is 1-amenable in the sense of "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"0806.4643","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2008-06-28T02:31:57Z","cross_cats_sorted":[],"title_canon_sha256":"ddae30e3e3f66cd5900a289063bdf83075ad409f739c0bb74d7aab0f4b4742b1","abstract_canon_sha256":"be3455375a3cabc931b92119b1ee5cb9ba4c61719b87936061bd4ab2f70ece62"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:03:54.824161Z","signature_b64":"LhFB7Lt3b3GYwFbMecYSEJInmjmWmpSoHfvNZMD0kSBM/LKkhWEPK96ob/yh39XMXxtB3uCSx3z1Xn3LPDzIAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"161c9ed09150f7cb162336ed7a5f202f43b6302e2e2783616eba13f4308bf7f9","last_reissued_at":"2026-05-18T04:03:54.823432Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:03:54.823432Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Norm one idempotent cb-multipliers with applications to the Fourier algebra in the cb-multiplier norm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Brian E. 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