TY  - JOUR
ID  - ArizmendiPeimbert2012
LB  - ArizmendiPeimbert2012
AU  - Arizmendi-Peimbert, Hugo
AU  - Carrillo-Hoyo, Angel
AU  - Roa-Fajardo, Jairo
TI  - On the extended and Allan spectra and topological radii
ST  - On the extended and Allan spectra and topological radii
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2012
VL  - 32
IS  - 2
SP  - 227
EP  - 234
DO  - http://dx.doi.org/10.7494/OpMath.2012.32.2.227
UR  - http://dx.doi.org/10.7494/OpMath.2012.32.2.227
AB  - In this paper we prove that the extended spectrum \(\Sigma(x)\), defined by W. Żelazko, of an element \(x\) of a pseudo-complete locally convex unital complex algebra \(A\) is a subset of the spectrum \(\sigma_A(x)\), defined by G.R. Allan. Furthermore, we prove that they coincide when \(\Sigma(x)\) is closed. We also establish some order relations between several topological radii of \(x\), among which are the topological spectral radius \(R_t(x)\) and the topological radius of boundedness \(\beta_t(x)\).
KW  - topological algebra
KW  - bounded element
KW  - spectrum
KW  - pseudocomplete algebra
KW  - topologically invertible element
KW  - extended spectral radius
KW  - topological spectral radius
SN  - 1232-9274
ER  -