Spectrally bounded  -derivations on Banach algebras |
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| Authors: | Tsiu-Kwen Lee Cheng-Kai Liu |
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| Affiliation: | Department of Mathematics, National Taiwan University, Taipei 106, Taiwan ; Department of Mathematics, National Taiwan University, Taipei 106, Taiwan |
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| Abstract: | Applying the density theorem on algebras with  -derivations, we show that if a  -derivation  of a unital Banach algebra  is spectrally bounded, then ![$[delta (A), A]subseteq text{rad}(A)$](http://www.ams.org/proc/2005-133-05/S0002-9939-04-07655-5/gif-abstract0/img5.gif) . Also,  if and only if  , where  denotes the spectral radius of  . |
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| Keywords: | Radical $phi $--derivation Banach algebra spectrally bounded mapping |
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