Harmonic analysis and automatic continuity in the context of generalized differential subalgebras
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909828137353216 |
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| author | Flores, Felipe I. |
| author_facet | Flores, Felipe I. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_05569 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Harmonic analysis and automatic continuity in the context of generalized differential subalgebras Flores, Felipe I. Functional Analysis Operator Algebras Primary 46K05, Secondary 46H30, 46H40 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. |
| title | Harmonic analysis and automatic continuity in the context of generalized differential subalgebras |
| topic | Functional Analysis Operator Algebras Primary 46K05, Secondary 46H30, 46H40 |
| url | https://arxiv.org/abs/2508.05569 |