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On the extended and Allan spectra and topological radii

2012; AGH University of Science and Technology; Volume: 32; Issue: 2 Linguagem: Inglês

10.7494/opmath.2012.32.2.227

2300-6919

Hugo Arizmendi-Peimbert, Angel Carrillo-Hoyo, Jairo Roa-Fajardo,

Holomorphic and Operator Theory

In this paper we prove that the extended spectrum Σ (x), defined by W. Żelazko, of an element x of a pseudo-complete locally convex unital complex algebra A is a subset of the spectrum σA(x), defined by G.R. Allan.Furthermore, we prove that they coincide when Σ(x) is closed.We also establish some order relations between several topological radii of x, among which are the topological spectral radius Rt(x) and the topological radius of boundedness βt(x).