Abstract
In this paper a characterization is obtained of those bounded operators on a Hilbert space at which the spectrum is continuous, where the spectrum is considered as a function whose domain is the set of all operators with the norm topology and whose range is the set of compact subsets of the plane with the Hausdorff metric. Similar characterizations of the points of continuity of the Weyl spectrum, the spectral radius, and the essential spectral radius are also obtained.
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The first author was supported by National Science Foundation Grant MCS 77-28396.
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Conway, J.B., Morrel, B.B. Operators that are points of spectral continuity. Integr equ oper theory 2, 174–198 (1979). https://doi.org/10.1007/BF01682733
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DOI: https://doi.org/10.1007/BF01682733