Harmonic analysis and automatic continuity in the context of generalized differential subalgebras
Harmonic analysis and automatic continuity in the context of generalized differential subalgebras
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 even properties of automatic continuity.
Felipe I. Flores
数学
Felipe I. Flores.Harmonic analysis and automatic continuity in the context of generalized differential subalgebras[EB/OL].(2025-08-07)[2025-08-18].https://arxiv.org/abs/2508.05569.点此复制
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