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Communications in Mathematical Physics

, Volume 61, Issue 3, pp 261–266 | Cite as

Unbounded derivations of commutativeC*-algebras

  • C. J. K. Batty
Article

Abstract

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.

Keywords

Neural Network Statistical Physic Complex System Nonlinear Dynamics Quantum Computing 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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    Bratteli, O., Robinson, D.W.: Unbounded derivations ofC*-algebras. Commun. math. Phys.42, 253–268 (1975)CrossRefGoogle Scholar
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    Sakai, S.: The theory of unbounded derivations inC*-algebras. Preprint, Copenhagen University Lecture Notes (1977)Google Scholar

Copyright information

© Springer-Verlag 1978

Authors and Affiliations

  • C. J. K. Batty
    • 1
  1. 1.Mathematical InstituteUniversity of OxfordOxfordEngland

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