Almost-everywhere discontinuity of the spectral radius

Ransford, Thomas

doi:10.1090/S0002-9939-00-05617-3

Almost-everywhere discontinuity of the spectral radius
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by Thomas J. Ransford PDF

Proc. Amer. Math. Soc. 129 (2001), 749-751 Request permission

Abstract:

Let $\rho (T)$ denote the spectral radius of an operator $T$. We construct operators $S$ and $T$ on $\ell ^2$ such that $\lambda \mapsto \rho (T-\lambda S)$ is discontinuous almost everywhere on the unit disk.

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