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Quasisimilarity‐invariance of joint spectra for certain subnormal tuples
Author(s) -
Athavale Ameer
Publication year - 2008
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdn054
Subject(s) - tuple , mathematics , spectrum (functional analysis) , unit sphere , unit (ring theory) , essential spectrum , taylor series , class (philosophy) , joint (building) , unit disk , pure mathematics , mathematical analysis , discrete mathematics , computer science , physics , mathematics education , quantum mechanics , artificial intelligence , architectural engineering , engineering
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 .