On joint spectra of non-commuting normal operators. (English) Zbl 0810.47003

Pryde, Alan J.; Sołtysiak, Andrzej

Bull. Aust. Math. Soc. 48, No. 1, 163-170 (1993).

Summary: 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.

MSC:

47A13	Several-variable operator theory (spectral, Fredholm, etc.)
47B15	Hermitian and normal operators (spectral measures, functional calculus, etc.)

Keywords:

Harte spectrum; bicommutant spectrum; \(n\)-tuple of normal Hilbert space operators; spectral set \(\gamma\)

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