About the joint spectrum of vector-valued functions

Mart Abel

doi:10.12697/ACUTM.2020.24.10

Mart Abel School of Digital Technologies, Tallinn University, Narva 25, 10120 Tallinn, Estonia; Institute of Mathematics and Statistics, University of Tartu, Narva 18, 51009 Tartu, Estonia https://orcid.org/0000-0003-0289-790X

DOI: https://doi.org/10.12697/ACUTM.2020.24.10

Keywords: unital topological algebra, joint spectrum, A-valued spectrum, equicontinuity, uniform closedness, uniform boundedness

Abstract

We generalize the results of Abtahi and Farhangi about the joint spectrum and A-valued spectrum of a vector-valued map from the class of unital commutative semisimple Banach algebras to the case of unital topological algebras.

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