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On the joint spectral radii of commuting Banach algebra elements

100%
EN
Some inequalities are proved between the geometric joint spectral radius (cf. [3]) and the joint spectral radius as defined in [7] of finite commuting families of Banach algebra elements.
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On joint spectral radii in locally convex algebras

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EN
We present several notions of joint spectral radius of mutually commuting elements of a locally convex algebra and prove that all of them yield the same value in case the algebra is pseudo-complete. This generalizes a result proved by the author in 1993 for elements of a Banach algebra.
EN
Agrafeuil and Zarrabi in [1] characterized all closed ideals with at most countable hull in a unital Banach algebra embedded in the classical disc algebra and satisfying certain conditions ((H1), (H2), (H3)), and the analytic Ditkin condition. We modify Ditkin’s condition and show that analogous result is true for a wider class of algebras. This is an extension of the result obtained in [1].
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Spectral radius formula for commuting Hilbert space operators

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EN
A formula is given for the (joint) spectral radius of an n-tuple of mutually commuting Hilbert space operators analogous to that for one operator. This gives a positive answer to a conjecture raised by J. W. Bunce in [1].
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Spectrum of generators of a noncommutative Banach algebra

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Existence of a multiplicative functional and joint spectra

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On the left and right joint spectra in Banach algebras

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Joint spectra and multiplicative functionals

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Approximate point joint spectra and multiplicative functionals

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