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Proceedings of the American Mathematical Society

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On the joint spectrum and $ H\sp \infty$-functional calculus for pairs of commuting contractions


Author: Alfredo Octavio
Journal: Proc. Amer. Math. Soc. 114 (1992), 497-503
MSC: Primary 47A13; Secondary 47A10, 47A60
DOI: https://doi.org/10.1090/S0002-9939-1992-1069294-1
MathSciNet review: 1069294
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Abstract: In this paper we show the existence of a pair of commuting completely nonunitary contractions $ (S,T)$ on a Hilbert space, whose joint Taylor spectrum contains the torus, such that there is a bounded analytic function $ h$ on the bidisk with $ h(S,T) = 0$.


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DOI: https://doi.org/10.1090/S0002-9939-1992-1069294-1
Keywords: Contractions, joint spectrum, functional calculus
Article copyright: © Copyright 1992 American Mathematical Society