Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 5 min ago
PreprintCC BY 4.0arXiv

Inner Products and Banach Algebra structures on Bicomplex Numbers and Their Associated Spaces

  • Prabhat Kumar
  • Fahed Zulfeqarr
  • Amit Ujlayan
  • Anjali Anjali
  • Akhil Prakash
  • M. Younus Bhat
Open at sourcePDFDOICite

Abstract

In this paper, we introduce various types of inner products and norms on the bicomplex number system ℂ2, the bicomplex vector space ℂ2n, the space of bicomplex matrices C2m × n, and the space of bicomplex polynomials ℂ2[ξ]n. We investigate the relationships among these inner products and norms, and establish several results. Furthermore, we prove that ℂ2 and ℂ2n 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.

Related

  1. Extending structures for the linear framework of Universal Algebra with applications to transposed Poisson algebras
    Changhuan Liu, Tingfeng Wan, Guodong Zhou
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  2. Infinite Series About Reciprocal Products of Fibonacci and Lucas Numbers
    Marta Na Chen, Wenchang Chu
    AxiomsPeer-reviewedCC BY 4.0Algebra & number theoryCrossref
  3. DG Algebra Structures on Mapping Cones with an Application to Edge Ideals
    Hugh Geller, Desiree Martin, Matthew Mastroeni +1
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryCombinatorics & discrete mathematicsarXiv
  4. The Quillen and sharbly Hopf algebra structures on Steinberg homology coincide
    Urshita Pal, Sam Payne
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryGeometry & topologyarXiv
  5. ℓ2-Betti numbers and Σ-invariants of graph products of cyclic groups and their automorphisms
    Marcos Escartín-Ferrer
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv

Cite

BibTeXRIS
BibTeX
@misc{kumar2026inner,
  title = {{Inner Products and Banach Algebra structures on Bicomplex Numbers and Their Associated Spaces}},
  author = {Prabhat Kumar and Fahed Zulfeqarr and Amit Ujlayan and Anjali Anjali and Akhil Prakash and M. Younus Bhat},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2607.06543},
  eprint = {2607.06543},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.06543},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Inner Products and Banach Algebra structures on Bicomplex Numbers and Their Associated Spaces
AU  - Prabhat Kumar
AU  - Fahed Zulfeqarr
AU  - Amit Ujlayan
AU  - Anjali Anjali
AU  - Akhil Prakash
AU  - M. Younus Bhat
PY  - 2026
DA  - 2026/10/14
PB  - arXiv
DO  - 10.48550/arxiv.2607.06543
UR  - https://arxiv.org/abs/2607.06543
AB  - In this paper, we introduce various types of inner products and norms on the bicomplex number system ℂ_2, the bicomplex vector space ℂ_2^n, the space of bicomplex matrices C_2^m × n, and the space of bicomplex polynomials ℂ_2[ξ]_n. We investigate the relationships among these inner products and norms, and establish several results. Furthermore, we prove that ℂ_2 and 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.
ER  -