Quasisimilarity-invariance of joint spectra for certain subnormal tuples

Abstract

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 B-2m in C-m. We show, in particular, that a subnormal m-tuple that is quasisimilar to either the Szego tuple or the Bergman tuple has its Taylor spectrum equal to the closure B-2m of B-2m and its essential Taylor spectrum equal to the unit sphere S2m-1, the topological boundary of B-2m. A parallel investigation goes through for a class of subnormal tuples associated with the open unit polydisk D-m in C-m.