Let D = G/K be an irreducible bounded symmetric domain of dimension d and let Hv(D) be the analytic continuation of the weighted Bergman spaces of holomorphic functions on D. We consider the d-tuple M = (M1,...,Md) of multiplication operators by coordinate functions and consider its spectral properties. We find those parameters v for which the tuple M is subnormal and we answer some open questions of Bagchi and Misra. In particular, we prove that when D = Bd is the unit ball in ℂd, then Bd is a k-spectral set of M if and only if Hv(Bd) is the Hardy space or a weighted Bergman space.
|Number of pages||23|
|Journal||Journal of Functional Analysis|
|State||Published - 1 Aug 2003|
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