S. M. Hamid

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Articles: 1

Multi-Dimensional Matrix Characterization of $(\mathcal{L}_{1},\mathcal{L}_{1})$ and Mercerian-type Theorem via Matrix Product

MFAT 31 (2025), no. 1, 30-38

30-38

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.

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