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Mathematische Annalen

, Volume 313, Issue 4, pp 609–616 | Cite as

Elementary operators on antiliminal \(C^*\)-algebras

  • Robert J. Archbold
  • Martin Mathieu
  • Douglas W.B. Somerset

Abstract.

We establish the equivalence of the following three properties of a \(C^*\)-algebra A. (a) Every positive elementary operator on A is completely positive. (b) The norm and the cb-norm coincide for every elementary operator on A. (c) A is an extension of an antiliminal \(C^*\)-algebra by an abelian one.

Mathematics Subject Classification (1991):47B47, 46L05 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Robert J. Archbold
    • 1
  • Martin Mathieu
    • 2
  • Douglas W.B. Somerset
    • 1
  1. 1. Department of Mathematical Sciences, University of Aberdeen, Aberdeen AB24 3UE, Scotland (e-mail: r.archbold@maths.abdn.ac.uk/ds@maths.abdn.ac.uk) GB
  2. 2. Department of Pure Mathematics, School of Mathematics and Physics, The Queen's University of Belfast, Belfast BT7 1NN, Northern Ireland (e-mail: m.m@qub.ac.uk) IE

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