The non-emptiness of joint spectral subsets of euclidean n-space

W. J. Ricker, A. R. Schep
1989 Journal of the Australian Mathematical Society  
A. Mclntosh and A. Pryde introduced and gave some applications of a notion of "spectral set", y(T), associated with each finite, commuting family of continuous linear operators T in a Banach space. Unlike most concepts of joint spectrum, the set y(T) is part of real Euclidean space. It is shown that y(T) is always non-empty whenver there are at least two operators in T.
doi:10.1017/s1446788700031724 fatcat:xhaloolojbcfbcq7mgyq3ks5ty