Homogeneous multiplication operators on bounded symmetric domains

Jonathan Arazy, Genkai Zhang

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)44-66
Number of pages23
JournalJournal of Functional Analysis
Issue number1
StatePublished - 1 Aug 2003

ASJC Scopus subject areas

  • Analysis


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