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Schwarz inequalities and the decomposition of positive maps on C*-algebras

Published online by Cambridge University Press:  24 October 2008

A. Guyan Robertson
A. Guyan Robertson
Affiliation:
Department of Mathematics, University of Edinburgh, Edinburgh EH9 3JZ
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Extract

In recent years there has been considerable progress in the study of certain linear maps of C*-algebras which preserve the natural partial ordering. The most tractable such maps, the completely positive ones, have proved to be of great importance in the structure theory of C*-algebras(4). However general positive (order-preserving) linear maps are (at present) very intractable. For example, there is no algebraic formula which enables one to construct a general positive map, even on the algebra of 3 3 complex matrices. It is therefore of interest to study conditions stronger than positivity, but weaker than complete positivity.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 94 , Issue 2 , September 1983 , pp. 291 - 296
Copyright
Copyright © Cambridge Philosophical Society 1983

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References

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