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

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.


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


[1] Fong, Studia Math. 81 pp 213– (1985)
[2] Dash, Pacific J. Math 64 pp 119– (1976) · Zbl 0329.47001
[3] Curto, Rev. Roumaine Math. Pures Appl. 31 pp 203– (1968)
[4] DOI: 10.1016/0022-1236(70)90055-8 · Zbl 0233.47024
[5] Müller, Studia Math 93 pp 87– (1989)
[6] Halmos, Finite-dimensional vector spaces (1958)
[7] Müller, Comment. Math. Univ. Carolin. 29 pp 255– (1988)
[8] DOI: 10.1512/iumj.1987.36.36024 · Zbl 0694.47015
[9] McIntosh, Proc. Centre Math. Anal. Austral. Nat. Univ. 9 pp 212– (1985)
[10] Harte, Proc. Roy. Irish Acad. Sect. A 72 pp 89– (1972)
[11] McIntosh, Studia Math. 88 pp 23– (1988)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.