Acta Mathematica Sinica, English Series

, Volume 24, Issue 11, pp 1891–1900 | Cite as

Noncommutative versions of the Singer-Wermer conjecture with linear left ϑ-derivations

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Abstract

The noncommutative Singer-Wermer conjecture states that every linear (possibly unbounded) derivation on a (possibly noncommutative) Banach algebra maps into its Jacobson radical. This conjecture is still an open question for more than thirty years. In this paper we approach this question via linear left ϑ-derivations.

Keywords

linear left ϑ-derivation linear ϑ-derivation Jacobson radical nil radical 

MR(2000) Subject Classification

46H99 47B47 
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Copyright information

© Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag GmbH 2008

Authors and Affiliations

  1. 1.Department of MathematicsSun Moon UniversityAsan, ChungnamKorea
  2. 2.Department of Mathematics EducationSeowon UniversityCheongju, ChungbukKorea

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