Rudol, Krzysztof Separation property and uniqueness of some spectra on \(H^ \infty\). (English) Zbl 0815.46043 Bull. Pol. Acad. Sci., Math. 41, No. 1, 51-54 (1993). 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 Keywords:uniqueness of joint spectral systems on algebras of bounded analytic functions; separation property of the maximal ideal spaces; functional calculi of the Sz.-Nagy-Foias type PDFBibTeX XMLCite \textit{K. Rudol}, Bull. Pol. Acad. Sci., Math. 41, No. 1, 51--54 (1993; Zbl 0815.46043)