Abstract
The purpose of the paper is to show that the Harte spectrum and the bicommutant spectrum of an arbitrary n−tuple of normal Hilbert space operators can be obtained from the spectral set γ introduced by McIntosh and Pryde. It is also proved that many commonly used joint spectra of an n−tuple of normal m by m matrices are equal. These results are non-commutative variants of some theorems proved by McIntosh, Pryde, and Ricker for commuting sets of operators.
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