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Currently displaying 1 – 2 of 2

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Applications of the scarcity theorem in ordered Banach algebras

Sonja Mouton — 2014

Studia Mathematica

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

Sonja Mouton — 2021

Czechoslovak Mathematical Journal

By considering arbitrary mappings $ω$ from a Banach algebra $A$ into the set of all nonempty, compact subsets of the complex plane such that for all $a \in A$ , 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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