Abstract
We investigate relations between different forms of subadditivity and submultiplicativity of the spectral radius. In particular, we prove that if the spectral radius is uniformly continuous on a Banach algebra, then the algebra is commutative modulo the radical; this confirms a conjecture raised by the second author in [7].
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Pták, V., Zemánek, J. On uniform continuity of the spectral radius in Banach algebras. Manuscripta Math 20, 177–189 (1977). https://doi.org/10.1007/BF01170724
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DOI: https://doi.org/10.1007/BF01170724