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On the reflexivity of pairs of contractions

Authors: Marek Kosiek, Alfredo Octavio and Marek Ptak
Journal: Proc. Amer. Math. Soc. 123 (1995), 1229-1236
MSC: Primary 47D27; Secondary 47A15, 47A20, 47A65
MathSciNet review: 1231037
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Abstract: We consider pairs of commuting contractions such that the joint left essential spectrum is dominating for the algebra $ {H^\infty }({{\mathbf{D}}^2})$. It is also assumed, in the first case, that one of them is $ {{\mathbf{C}}_{0 \cdot }}$ and the second one is absolutely continuous. In the second case, we assume that the pair is diagonally extendable. It will be shown that such pairs are reflexive.

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Keywords: Essential spectrum, reflexive algebras, reflexive operators
Article copyright: © Copyright 1995 American Mathematical Society