Spectral radius characterization of commutativity in Banach algebras
Jaroslav Zemánek (1977)
Studia Mathematica
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Displaying similar documents to “Counterexample on semiradial Banach algebras”
Spectral radius characterization of commutativity in Banach algebras
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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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In ordered Banach algebras, we introduce eventually and asymptotically positive elements. We give conditions for the following spectral properties: the spectral radius belongs to the spectrum (Perron--Frobenius property); the spectral radius is the only element in the peripheral spectrum; there are positive (approximate) eigenvectors for the spectral radius. Recently such types of results have been shown for operators on Banach lattices. Our results can be viewed as a complement, since...
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In this paper we suggest a general framework of the spectral mapping theorem in terms of parametrized Banach space bicomplexes.