Czechoslovak Mathematical Journal, first online, pp. 1-19
Generalized spectral perturbation and the boundary spectrum
Received February 4, 2020. Published online February 2, 2021.
Abstract: By considering arbitrary mappings $\omega$ 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 $\omega(a)$ 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.