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On the continuity of derivations over locally regular Banach algebras
- Part of
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- Journal:
- Canadian Mathematical Bulletin , First View
- Published online by Cambridge University Press:
- 06 March 2026, pp. 1-12
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- Article
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We study the problem of continuity of derivations over Banach algebras. More specifically, we consider derivations over a class of Banach algebras that contain dense “
$C^*$-like” subalgebras. The results we prove are then applied to 
$L^p$-crossed products and symmetrized 
$L^p$-crossed products. For example, it follows 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.
