Hostname: page-component-7479d7b7d-qs9v7 Total loading time: 0 Render date: 2024-07-08T23:50:12.698Z Has data issue: false hasContentIssue false
  • English
  • Français

On the boundary spectrum in banach algebras

Published online by Cambridge University Press:  17 April 2009

S. Mouton
S. Mouton
Affiliation:
Department of Mathematical Sciences, University of Stellenbosch, Private Bag X1, Matieland 7602, South Africa e-mail: smo@sun.ac.za
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We investigate some properties of the set S∂(a) = {λ ∈ ℂ: λ – a ∈ ∂S} (which we call the boundary spectrum of a) where ∂S denotes the topological boundary of the set S of all non-invertible elements of a Banach algebra A, and where a is an element of A.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 74 , Issue 2 , October 2006 , pp. 239 - 246
Copyright
Copyright © Australian Mathematical Society 2006

References

[1]Aupetit, B., A primer on spectral theory (Springer–Verlag, New York, 1991).CrossRefGoogle Scholar
[2]Bonsall, F.F. and Duncan, J., Complete normed algebras (Springer–Verlag, New York, 1973).Google Scholar
[3]Halmos, P.R., A Hilbert space problem book (Springer–Verlag, New York, 1982).Google Scholar
[4]du, H.Mouton, T. and Mouton, S., ‘Domination properties in ordered Banach algebras’, Studia Math. 149 (2002), 63–73.Google Scholar
[5]Mouton, S., ‘Convergence properties of positive elements in Banach algebras’, Math. Proc. R. Ir. Acad. 102A (2002), 149–162.Google Scholar
[6]Mouton, S., ‘A spectral problem in ordered Banach algebras’, Bull. Austral. Math. Soc. 67 (2003), 131–144.CrossRefGoogle Scholar
[7]Mouton, S., ‘On spectral continuity of positive elements’, Studia Math. 174 (2006), 75–84.Google Scholar
[8]Mouton, S. (née Rode) and Raubenheimer, H., ‘More spectral theory in ordered Banach algebras’, Positivity 1 (1997), 305–317.Google Scholar
[9]Raubenheimer, H. and Rode, S., ‘Cones in Banach algebras’, Indag. Math. (N.S.) 7 (1996), 489–502.CrossRefGoogle Scholar
[10]Taylor, A.E. and Lay, D.C., Introduction to functional analysis (Krieger, Florida, 1986).Google Scholar