Some uses of subharmonicity in functional analysis

Bernard Aupetit

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Laura Burlando (1994)

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This survey deals with necessary and/or sufficient conditions for continuity of the spectrum and spectral radius functions at a point of a Banach algebra.

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Perturbation and spectral discontinuity in Banach algebras

Rudi Brits (2011)

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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...

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