Applications of the scarcity theorem in ordered Banach algebras
We apply Aupetit's scarcity theorem to obtain stronger versions of many spectral-theoretical results in ordered Banach algebras in which the algebra cone has generating properties.
Generalized spectral perturbation and the boundary spectrum
By considering arbitrary mappings from a Banach algebra into the set of all nonempty, compact subsets of the complex plane such that for all , the set lies between the boundary and connected hull of the exponential spectrum of , 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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