Journal of Operator Theory

Volume 57, Issue 1, Winter 2007 pp. 121-145.

Some formulae for norms of elementary operators

Authors: Richard M. Timoney
Author institution: School of Mathematics, Trinity College, Dublin 2, Ireland

Summary: We present a formula for the norm of an elementary operator on a $C^*$-algebra that seems to be new. The formula involves (matrix) numerical ranges and a kind of geometrical mean for positive matrices, the tracial geometric mean, which seems not to have been studied previously and has interesting properties. In addition, we characterise compactness of elementary operators.

Keywords: Tracial geometric mean, matrix numerical range, $C^*$-algebra.

Contents Full-Text PDF