ON JOINT SPECTRA OF NON-COMMUTING NORMAL OPERATORS

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 gamma 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.