Quasisimilarity‐invariance of joint spectra for certain subnormal tuples

We investigate the invariance of the joint Taylor spectrum and the joint essential Taylor spectrum under quasisimilarity in the context of a special class of subnormal operator tuples associated with the open unit ball 2 m in ℂ m . We show, in particular, that a subnormal m ‐tuple that is quasisimilar to either the Szegö tuple or the Bergman tuple has its Taylor spectrum equal to the closureB 2 m¯of 2 m and its essential Taylor spectrum equal to the unit sphere 2 m −1 , the topological boundary of 2 m . A parallel investigation goes through for a class of subnormal tuples associated with the open unit polydisk ; m in ℂ m .