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The norm of a symmetric elementary operator

Author: Bojan Magajna
Journal: Proc. Amer. Math. Soc. 132 (2004), 1747-1754
MSC (2000): Primary 47B47
Published electronically: October 8, 2003
MathSciNet review: 2051136
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Abstract: The norm of the operator $x\mapsto a^*xb+b^*xa$ on $A= {\mathrm B}(\mathcal{H})$(or on any prime C$^*$-algebra $A$) is computed for all $a,b\in A$ and is shown to be equal to the completely bounded norm.

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Additional Information

Bojan Magajna
Affiliation: Department of Mathematics, University of Ljubljana, Jadranska 19, Ljubljana 1000, Slovenia

Keywords: Elementary operator, completely bounded map
Received by editor(s): July 19, 2002
Received by editor(s) in revised form: February 7, 2003
Published electronically: October 8, 2003
Additional Notes: Supported by the Ministry of Science and Education of Slovenia
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2003 American Mathematical Society

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