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Peer-reviewedCC BY 4.0Axioms

Matrix Transformations and Scale Separation in Non-Archimedean λ-Almost Convergent Sequence Spaces

  • Richard F. Patterson1
  • Ekrem Savaş2
  • Sami M. Hamid1
  1. 1Department of Mathematics and Statistics, University of North Florida, Jacksonville, FL 32224, USA
  2. 2Faculty of Engeering, Ostim Technical University, 06374 Ankara, Turkey
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Abstract

Let F be a complete, non-trivially valued, non-Archimedean field of characteristic zero. This paper studies the space V^λ of λ-almost convergent sequences over F and its paranormed generalization V^λ(p), establishing it as a complete non-Archimedean topological vector space for every admissible λ. The classical inclusion c⊂V^λ holds if and only if F has residue characteristic zero and m−λm is unbounded. The matrix class (c,V^λ) is characterized by means of an ultrametric gliding hump argument. The strong almost space [V^,λ] and the almost λ-statistical space s^λ coincide on l∞, yet over Qp this common space is not contained in V^λ, a separation that reflects the arithmetic of the base field.

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Cite

BibTeXRIS
BibTeX
@article{patterson2026matrix,
  title = {{Matrix Transformations and Scale Separation in Non-Archimedean λ-Almost Convergent Sequence Spaces}},
  author = {Richard F. Patterson and Ekrem Savaş and Sami M. Hamid},
  journal = {Axioms},
  year = {2026},
  month = oct,
  doi = {10.3390/axioms15100752},
  url = {https://www.mdpi.com/2075-1680/15/10/752},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Matrix Transformations and Scale Separation in Non-Archimedean λ-Almost Convergent Sequence Spaces
AU  - Richard F. Patterson
AU  - Ekrem Savaş
AU  - Sami M. Hamid
PY  - 2026
DA  - 2026/10/09
JO  - Axioms
DO  - 10.3390/axioms15100752
UR  - https://www.mdpi.com/2075-1680/15/10/752
AB  - Let F be a complete, non-trivially valued, non-Archimedean field of characteristic zero. This paper studies the space V^λ of λ-almost convergent sequences over F and its paranormed generalization V^λ(p), establishing it as a complete non-Archimedean topological vector space for every admissible λ. The classical inclusion c⊂V^λ holds if and only if F has residue characteristic zero and m−λm is unbounded. The matrix class (c,V^λ) is characterized by means of an ultrametric gliding hump argument. The strong almost space [V^,λ] and the almost λ-statistical space s^λ coincide on l∞, yet over Qp this common space is not contained in V^λ, a separation that reflects the arithmetic of the base field.
SN  - 2075-1680
ER  -