Applications of the growth characteristics induced by the spectral distance |
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Authors: | Rudi Brits |
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Affiliation: | Department of Mathematics, University of Johannesburg, Aucklandpark 6000, Johannesburg, South Africa. |
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Abstract: | 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 Phragm´en-Lindel¨of 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. |
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Keywords: | Asymptotically intertwined commutator spectral distance quasinilpotent equivalent |
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