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Separation property and uniqueness of some spectra on \(H^ \infty\). (English) Zbl 0815.46043

Summary: The uniqueness of joint spectral systems on algebras of bounded analytic functions is obtained as a consequence of the separation property of the maximal ideal spaces. This property, shown for the unit disc by F. D. Suarez, holds for a wider class of plane domains. These results are applicable to spectral theory of functional calculi of the Sz.-Nagy-Foias type.

MSC:

46J15 Banach algebras of differentiable or analytic functions, \(H^p\)-spaces
46H30 Functional calculus in topological algebras
30D50 Blaschke products, etc. (MSC2000)
47D99 Groups and semigroups of linear operators, their generalizations and applications
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