What is an example of a $C^{*}$ algebra such that the span of nilpotent elements is not a sub vector space of the span of commutator elements. Obviously any such $C^{*}$ algebra would be a counter example to the question $2$ of the following MO post: https://mathoverflow.net/questions/231328/the-saturation-of-murray-von-neumann-relation I know that every stable $C^{*}$ algebra or […]

Is there a reference which studied the K theory of finite dimensional Banach algebras? In particular is there a finite dimensional Banach algebra whose $K_{0}$-group is a non trivial finite group?(I am Sorry if the later question is elementary) Edit: What is a generalization of the following theorem by Taylor, to non commutative Banach algebras(In […]

I’m trying to investigate the notion of primitive spectrum and its so-called Jacobson or hull-kernel topology, but I can only find references which define it for C*-algebras: see the Wikipedia page “Spectrum of a C*-algebra” for the definition I’m talking about. It seems like this definition would make sense for any (let’s stick with unital) […]

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