Reflexivity for Subnormal Systems With Dominating Spectrum in Product Domains |
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Authors: | Jörg Eschmeier |
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Institution: | 1.Fachrichtung Mathematik,Universit?t des Saarlandes,Saarbrücken,Germany |
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Abstract: | The question whether every subnormal tuple
on a complex Hilbert space is reflexive is one of the major open problems in multivariable invariant subspace theory. Positive
answers have been given for subnormal tuples with rich spectrum in the unit polydisc or the unit ball. The ball case has been
extended by Didas 6] to strictly pseudoconvex domains. In the present note we extend the polydisc case by showing that every
subnormal tuple with pure components and rich Taylor spectrum in a bounded polydomain
is reflexive. |
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Keywords: | Primary 47A13 Secondary 47A15 47B20 |
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