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arXiv · 2306.15641

On $(p, q)-$centralizers of certain Banach algebras

M. J. Mehdipour·N. Salkhordeh
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Abstract

Let $A$ be an algebra with a right identity. In this paper, we study $(p, q)-$centralizers of $A$ and show that every $(p, q)-$centralizer of $A$ is a two-sided centralizer. In the case where, $A$ is normed algebra, we also prove that $(p, q)-$centralizers of $A$ are bounded. Then, we apply the results for some group algebras and verify that $L^1(G)$ has a nonzero weakly compact $(p, q)-$centralizer if and only if $G$ is compact and the center of $L^1(G)$ is non-zero. Finally, we investigate $(p, q)-$Jordan centralizers of $A$ and determine them.

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BibTeXRIS

M. J. Mehdipour, N. Salkhordeh. 2023-06-27. On $(p, q)-$centralizers of certain Banach algebras. https://arxiv.org/abs/2306.15641

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