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On joint spectral radii in locally convex algebras

Andrzej Sołtysiak — 2006

Studia Mathematica

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.

On a certain class of subspectra

Andrzej Sołtysiak — 1991

Commentationes Mathematicae Universitatis Carolinae

The aim of this paper is to characterize a class of subspectra for which the geometric spectral radius is the same and depends only upon a commuting n -tuple of elements of a complex Banach algebra. We prove also that all these subspectra have the same capacity.

Ditkin’s condition and ideals with at most countable hull in algebras of functions analytic in the unit disc

Andrzej SołtysiakAntoni Wawrzyńczyk — 2012

Commentationes Mathematicae

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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