A note on the singular spectrum.

L. Lindeboom (Groenewald); H. Raubenheimer

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Continuous characters and joint topological spectrum

Wiesław Żelazko (2007)

Control and Cybernetics

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Spectrum of generators of a noncommutative Banach algebra

Vladimír Müller, Andrzej Sołtysiak (1989)

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Approximate point joint spectra and multiplicative functionals

Andrzej Sołtysiak (1987)

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Topologically Invertible Elements and Topological Spectrum

Mati Abel, Wiesław Żelazko (2006)

Bulletin of the Polish Academy of Sciences. Mathematics

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Properties of topologically invertible elements and the topological spectrum of elements in unital semitopological algebras are studied. It is shown that the inversion $x \mapsto x^{- 1}$ is continuous in every invertive Fréchet algebra, and singly generated unital semitopological algebras have continuous characters if and only if the topological spectrum of the generator is non-empty. Several open problems are presented.

On the topological boundary of the one-sided spectrum

Vladimír Müller (1999)

Czechoslovak Mathematical Journal

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It is well-known that the topological boundary of the spectrum of an operator is contained in the approximate point spectrum. We show that the one-sided version of this result is not true. This gives also a negative answer to a problem of Schmoeger.