{
  "abstract": "Let $D$ be a unital separable $C^*$-algebra with a faithful state $σ$ and $G$ be a discrete group. We introduce a property called relative norm averaging property (RNA) for almost periodic $σ$-preserving actions by $G$ on $(D,σ)$. We prove that if an almost periodic $σ$-preserving action $α$ satisfies that $\\overline{α(G)} \\subseteq \\text{Aut}(D,σ)$ is connected and nontrivial, then $α$ satisfies (RNA). As an application, we prove that if $G$ has property PHP of Ozawa and $α:G\\curvearrowright (D,σ)$ is an ergodic (i.e. $D^G=\\mathbb{C}$) almost periodic $σ$-preserving action with $\\overline{α(G)}$ being connected, then $D\\rtimes_r G$ is selfless. This includes certain paradoxical isometric actions of $\\mathbb{F}_2$ on the sphere. In non-ergodic case, we prove that the relative norm averaging property implies that $D\\rtimes_r G$ satisfies the $D^G$-valued selfless, if $G$ satisfies PHP.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.35644",
  "author_total": 1,
  "authors": [
    {
      "name": "Ryo Toyota"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3zhnkam9y93xb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.35644",
  "fulltext_url": null,
  "id": "3zhnkam9y93xb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.35644",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.OA"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7223787474",
  "pdf_url": "https://arxiv.org/pdf/2610.35644",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3zhnkam9y93xb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.35644",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.35644"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Relative norm averaging property and selflessness of almost periodic actions",
  "title_text": "Relative norm averaging property and selflessness of almost periodic actions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/3zhnkam9y93xb",
  "venue": "arXiv",
  "versions": []
}