Unbounded derivations of commutativeC*-algebras
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It is shown that an unbounded *-derivation δ of a unital commutativeC*-algebraA is quasi well-behaved if and only if there is a dense open subsetU of the spectrum ofA such that, for anyf in the domain of δ, δ(f) vanishes at any point ofU wheref attains its norm. An example is given to show that even if δ is closed it need not be quasi well-behaved. This answers negatively a question posed by Sakai for arbitraryC*-algebras.
It is also shown that there are no-zero closed derivations onA if the spectrum ofA contains a dense open totally disconnected subset.
KeywordsNeural Network Statistical Physic Complex System Nonlinear Dynamics Quantum Computing
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