A class of spectral sets
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- by C. Robert Warner PDF
- Proc. Amer. Math. Soc. 57 (1976), 99-102 Request permission
Abstract:
The two main results are: (i) If the union and intersection of two closed sets are Ditkin sets, then each of the sets is a Ditkin set. (ii) If the union of two sets is a spectral set and their intersection is a Ditkin set, then each of the sets is a spectral set. A corollary of (i) is a generalization of a theorem due to Calderón which proved that closed polyhedral sets in ${R^n}$ are Ditkin (= Calderón) sets. A corollary of (ii) establishes an analogous result for spectral sets. The proofs hold for commutative semisimple regular Banach algebras which satisfy Ditkin’s condition-that the empty set and singletons are Ditkin sets in the maximal ideal space.References
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Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 57 (1976), 99-102
- MSC: Primary 43A45; Secondary 46J20
- DOI: https://doi.org/10.1090/S0002-9939-1976-0410275-7
- MathSciNet review: 0410275