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This research reveals localizations of Arens-Michael-Fréchet algebras in contractive quantum planes, indicating implications for Taylor and Putinar spectra.
In the present paper we investigate the localizations in the sense of J. L. Taylor of the Arens-Michael-Fréchet algebras occurred within the formal geometry of a contractive q-plane. It turns out that all noncommutative Fréchet algebras obtained by the Fréchet sheaves of the formal geometry are indeed localizations. That topological homology property of the structure sheaf results in the key properties of Taylor and Putinar spectra of the Banach q-modules.
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Anar Dosi (2025) studied this question.
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