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We show that for a commuting n-tuple of hermitian operators, with perfect spectrum, the essential centre of the algebra of operators commuting with the n-tuple mod a diagonalization ideal arises from the C *-algebra of the n-tuple. This answers a question for normal operators and the Hilbert– Schmidt class connected to K-theory for almost normal operators.

The Essential Centre of the mod a Diagonalization Ideal Commutant of an n-tuple of Commuting Hermitian Operators