Abstract
By considering arbitrary map**s ω from a Banach algebra A into the set of all nonempty, compact subsets of the complex plane such that for all a ∈ A, the set ω(a) lies between the boundary and connected hull of the exponential spectrum of a, we create a general framework in which to generalize a number of results involving spectra such as the exponential and singular spectra. In particular, we discover a number of new properties of the boundary spectrum.
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The author acknowledges, with thanks, financial support provided by the National Research Foundation (NRF) of South Africa (Grant Number 96130).
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Mouton, S. Generalized Spectral Perturbation and the Boundary Spectrum. Czech Math J 71, 603–621 (2021). https://doi.org/10.21136/CMJ.2021.0046-20
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DOI: https://doi.org/10.21136/CMJ.2021.0046-20
Keywords
- exponential spectrum
- singular spectrum
- boundary spectrum
- boundary and hull
- (strong) Riesz property
- Mobius spectrum