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arXiv · 2507.23696

On the continuity of derivations over locally regular Banach algebras

Felipe I. Flores
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Abstract

We study the problem of continuity of derivations over Banach algebras. More specifically, we consider a class of Banach algebras that contain a dense '$C^*$-like' subalgebra. We discuss applications to $L^p$-crossed products and symmetrized $L^p$-crossed products. As an example, our results imply that every derivation over the $L^p$-crossed product $F^p(G,X,\alpha)$ is continuous, provided that $G$ is infinite, finitely generated, has polynomial growth, and acts freely on the compact Hausdorff space $X$.

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Felipe I. Flores. 2025-07-31. On the continuity of derivations over locally regular Banach algebras. https://doi.org/10.4153/s0008439526101878

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