{
  "abstract": "In this paper, we introduce various types of inner products and norms on the bicomplex number system $\\mathbb{C}_2$, the bicomplex vector space ${\\mathbb{C}_2}^{n}$, the space of bicomplex matrices ${C_2}^{m \\times n}$, and the space of bicomplex polynomials $\\mathbb{C}_2[ξ]_n$. We investigate the relationships among these inner products and norms, and establish several results. Furthermore, we prove that $\\mathbb{C}_2$ and ${\\mathbb{C}_2}^{n}$ are Banach algebras and Hilbert spaces. These results provide a unified framework for the study of inner product structures and normed linear spaces over bicomplex numbers and their associated spaces.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.06543",
  "author_total": 6,
  "authors": [
    {
      "name": "Prabhat Kumar"
    },
    {
      "name": "Fahed Zulfeqarr"
    },
    {
      "name": "Amit Ujlayan"
    },
    {
      "name": "Anjali Anjali"
    },
    {
      "name": "Akhil Prakash"
    },
    {
      "name": "M. Younus Bhat"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bkx5jpct572yg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.06543",
  "fulltext_url": null,
  "id": "bkx5jpct572yg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.06543",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CV"
    ],
    [
      "arxiv",
      "math.FA"
    ],
    [
      "arxiv",
      "math.GN"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2604|Algebraic and Geometric Analysis"
    ]
  ],
  "openalex": "W7167711643",
  "pdf_url": "https://arxiv.org/pdf/2607.06543",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bkx5jpct572yg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2607.06543",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.06543"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.GN",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Inner Products and Banach Algebra structures on Bicomplex Numbers and Their Associated Spaces",
  "title_text": "Inner Products and Banach Algebra structures on Bicomplex Numbers and Their Associated Spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/bkx5jpct572yg",
  "venue": "arXiv",
  "versions": []
}