Abstract
This paper examines four-dimensional matrices in $(\mathcal{L}_{1},\mathcal{L}_{1})$ under standard matrix product. Using established characterizations of $(\mathcal{L}_{1},\mathcal{L}_{1};P)$, we demonstrate that $(\mathcal{L}_{1},\mathcal{L}_{1})$ forms a Banach algebra under standard matrix operations. We prove that $(\mathcal{L}_{1},\mathcal{L}_{1};P)$ is a closed, convex semigroup with identity under matrix product. Finally, we present a Mercerian-type theorem for four-dimensional matrices via matrix product.
Key words: Key words and phrases: Double sequences, Four-dimensional matrices,
Mercerian-type theorem.
Full Text
Article Information
| Title | Multi-Dimensional Matrix
Characterization of $(\mathcal{L}_{1},\mathcal{L}_{1})$ and Mercerian-type
Theorem via Matrix Product |
| Source | Methods Funct. Anal. Topology, Vol. 31 (2025), no. 1, 30-38 |
| DOI | 10.31392/MFAT-npu26_1.2025.03 |
| Milestones | Received 05/12/2024; Revised 07/01/2025 |
| Copyright | The Author(s) 2025 (CC BY-SA) |
Authors Information
Sami M. Hamid
Department of Mathematics & Statistics, University of North Florida, Jacksonville, FL 32224, USA
Richard F. Patterson
Department of Mathematics & Statistics, University of North Florida, Jacksonville, FL 32224, USA
Citation Example
Sami M. Hamid and Richard F. Patterson, Multi-Dimensional Matrix
Characterization of $(\mathcal{L}_{1},\mathcal{L}_{1})$ and Mercerian-type
Theorem via Matrix Product, Methods Funct. Anal. Topology 31
(2025), no. 1, 30-38.
BibTex
@article {MFAT2096,
AUTHOR = {Sami M. Hamid and Richard F. Patterson},
TITLE = {Multi-Dimensional Matrix
Characterization of $(\mathcal{L}_{1},\mathcal{L}_{1})$ and Mercerian-type
Theorem via Matrix Product},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {31},
YEAR = {2025},
NUMBER = {1},
PAGES = {30-38},
ISSN = {1029-3531},
DOI = {10.31392/MFAT-npu26_1.2025.03},
URL = {https://mfat.imath.kiev.ua/article/?id=2096},
}
