Quaestiones Mathematicae

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Applications of the growth characteristics induced by the spectral distance

Rudi Brits


Let A be a complex unital Banach algebra. Using a connection between the spectral distance and the growth characteristics of a certain entire map into A, we derive a generalization of Gelfand's famous power boundedness theorem. Elaborating on these ideas, with the help of a  Phragmén–Lindelöf device for subharmonic functions, it is then shown, as the main result, that two normal elements of a C*-algebra are equal if and only if they are quasinilpotent equivalent.

Keywords: Asymptotically intertwined, commutator, spectral distance, quasinilpotent equivalent
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