Spectral radius characterization of commutativity in Banach algebras
Jaroslav Zemánek (1977)
Studia Mathematica
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Displaying similar documents to “A note on criteria of Le Page and Hirschfeld-Żelazko for the commutativity of Banach algebras”
Spectral radius characterization of commutativity in Banach algebras
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Perturbation and spectral discontinuity in Banach algebras
Rudi Brits (2011)
Studia Mathematica
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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...