On the extended and Allan spectra and topological radii

• Autorzy: Arizmendi-Peimbert H. , Carrillo-Hoyo A. , Roa-Fajardo J.
• Języki publikacji: EN

Abstrakty

EN

In this paper we prove that the extended spectrum ∑(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 ∑ (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).

Słowa kluczowe

EN

topological algebra; bounded element; spectrum; pseudocomplete algebra; topologically invertible element; extended spectral radius; topological spectral radius

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2012
• Tom: Vol. 32, no. 2
• Strony: 227--234
• Opis fizyczny: Bibliogr. 4 poz.

Twórcy

autor

Arizmendi-Peimbert H.

autor

Carrillo-Hoyo A.

autor

Roa-Fajardo J.

• Universidad Nacional Autónoma de México Instituto de Matemáticas Ciudad Universitaria, México D.F. 04510 México,

Bibliografia

• [1] G.R. Allan, A spectral theory for locally convex algebras, Proc. London Math. Soc. (3) 15 (1965), 399–421.
• [2] H. Arizmendi, On the spectral radius of a matrix algebra, Funct. Approx. Comment. Math. 19 (1990), 167–176.
• [3] H. Arizmendi, A. Carrillo, On the extended spectral radius in B0-algebras, Funct. Approx. Comment. Math. 19 (1990), 77–81.
• [4] W. Żelazko, Selected topics in topological algebras, Aarhus University Lecture Notes Series 31 (1971).