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Reflexivity of N-tuples of contractions with rich joint left essential spectrum. (English) Zbl 0743.47032

Summary: It will be shown that the WOT-closed algebra generated by an \(N\)-tuple of doubly commuting contractions, for which the polydisc \(D^ N\) is a spectral set and whose joint left essential spectrum is dominating for the algebra \(H^ \infty(D^ N)\) is reflexive. The second version of our main result, instead of double commutativity, uses the membership of the class \(C_ 0\).

MSC:

47L30 Abstract operator algebras on Hilbert spaces
47A10 Spectrum, resolvent
47A25 Spectral sets of linear operators
47A15 Invariant subspaces of linear operators
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