Perturbation and spectral discontinuity in Banach algebras

• Autorzy: Rudi Brits
• Języki publikacji: EN

Abstrakty

EN

We extend an example of B. Aupetit, which illustrates spectral discontinuity for operators on an infinite-dimensional separable Hilbert space, to a general spectral discontinuity result in abstract Banach algebras. This can then be used to show that given any Banach algebra, Y, one may adjoin to Y a non-commutative inessential ideal, I, so that in the resulting algebra, A, the following holds: To each x ∈ Y whose spectrum separates the plane there corresponds a perturbation of x, of the form z = x + a where a ∈ I, such that the spectrum function on A is discontinuous at z.

Kategorie tematyczne

• 47A55: Perturbation theory
• 46H05: General theory of topological algebras
• 47A10: Spectrum, resolvent

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2011
• Tom: 203
• Numer: 3
• Strony: 253-263

Daty

wydano

2011

Twórcy

autor

Rudi Brits

• Department of Mathematics, University of Johannesburg, Johannesburg, South Africa

Identyfikatory

DOI

10.4064/sm203-3-3