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arXiv · 2508.05569

Harmonic analysis and automatic continuity in the context of generalized differential subalgebras

Felipe I. Flores
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Abstract

For appropriate parameters $k,p,q$, we introduce and systematically study the class of $(k,p,q)$-differential subalgebras. This is a vast class of Banach $^*$-algebras defined by their relation with their $C^*$-envelopes. Some examples are given by normable two-sided $^*$-ideals, domains of closed $^*$-derivations, full Hilbert algebras, and some weighted convolution algebras of various kinds. We prove that this class of algebras possesses various interesting properties, such as closedness under a functional calculus based on smooth functions, $^*$-regularity, Wiener's property $(W)$, and properties of automatic continuity.

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Felipe I. Flores. 2025-08-07. Harmonic analysis and automatic continuity in the context of generalized differential subalgebras. https://arxiv.org/abs/2508.05569

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