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On the norm of an inner derivation of a C*-algebra

Published online by Cambridge University Press:  24 October 2008

R. J. Archbold
R. J. Archbold
Affiliation:
The University of Aberdeen
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Extract

Let A be a C*-algebra with centre Z. If a ∈ A, the bounded linear mapping x → + ax – xa (x ∈ A) is called the inner derivation of A induced by a, and we denote it by D(a, A). A simple application of the triangle inequality shows that

where d (a; Z) denotes the distance from a to Z in the normed space A.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 84 , Issue 2 , September 1978 , pp. 273 - 291
Copyright
Copyright © Cambridge Philosophical Society 1978

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References

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