More on Restricted Boundaries
Year: 2025
Type: article
Abstract: In our paper [‘Linking the boundary and exponential spectra via the restricted topology’, J. Math. Anal. Appl. 454 (2017), 730–745], we defined and used the restricted topology to establish certain connections among the boundary spectrum, the exponential spectrum, the topological boundary of the spectrum and the connected hull of the spectrum, and in [‘The restricted connected hull: filling the hole’, Bull. Aust. Math. Soc. 109 (2024), 388–392], we presented further properties of the restricted connected hull. We now continue our investigation of the restricted boundary. In particular, we prove a number of mapping and regularity-type properties of the restricted boundary. In addition, we use this concept to provide a new characterisation of the Jacobson radical of a Banach algebra and a variation of Harte’s theorem. Finally, we establish spectral continuity results, in particular, in ordered Banach algebras.
Authors: SONJA MOUTON, ROBIN HARTE
Institution: Stellenbosch University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,550
OpenAlex ID: W4407609183