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A NOTE ON POSITIVITY OF ELEMENTARY OPERATORS

Published online by Cambridge University Press:  01 March 2000

RICHARD M. TIMONEY
RICHARD M. TIMONEY
Affiliation:
School of Mathematics, Trinity College, Dublin 2, Ireland
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Abstract

We show that operators on n × n matrices which are representable in the form T(X) = [sum ][lscr ]i=1aiXbi (where ai and bi are n × n matrices) and are k-positive for k = [√[lscr ]] must be completely positive. As a consequence, elementary operators on a C*-algebra with minimal length [lscr ] which are k-positive for k = [√[lscr ]] must be completely positive.

Type
NOTES AND PAPERS
Information
Bulletin of the London Mathematical Society , Volume 32 , Issue 2 , March 2000 , pp. 229 - 234
Copyright
© The London Mathematical Society 2000

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