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Finite generation in C*-algebras and Hilbert C*-modules

David P. Blecher, Tomasz Kania (2014)

Studia Mathematica

We characterize C*-algebras and C*-modules such that every maximal right ideal (resp. right submodule) is algebraically finitely generated. In particular, C*-algebras satisfy the Dales-Żelazko conjecture.

Finite spectra and quasinilpotent equivalence in Banach algebras

Rudi M. Brits, Heinrich Raubenheimer (2012)

Czechoslovak Mathematical Journal

This paper further investigates the implications of quasinilpotent equivalence for (pairs of) elements belonging to the socle of a semisimple Banach algebra. Specifically, not only does quasinilpotent equivalence of two socle elements imply spectral equality, but also the trace, determinant and spectral multiplicities of the elements must agree. It is hence shown that quasinilpotent equivalence is established by a weaker formula (than that of the spectral semidistance). More generally, in the second...

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