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Analysis demonstrates the continuity of derivations in Banach algebras with dense C-like subalgebras, suggesting implications for Lp-crossed products.
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 Lᵖ-crossed products and symmetrized Lᵖ-crossed products. As an example, our results imply that every derivation over the Lᵖ-crossed product Fᵖ(G,X,α) is continuous, provided that G is infinite, finitely generated, has polynomial growth, and acts freely on the compact space X.
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Felipe I. Flores (2025) studied this question.
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