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Perturbation and spectral discontinuity in Banach algebras

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Brits R.

Studia Mathematica

2011

tom 203

nr 3

253-263

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.

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1 Studia Mathematica

1 Brits R.

1 2011

Wyniki wyszukiwania

Perturbation and spectral discontinuity in Banach algebras