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We show that for a commuting n-tuple of hermitian operators, with perfectspectrum, the essential centre of the algebra of operators commuting with then-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 classconnected 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