Some Formulae for Norms of Elementary Operators

Mathematics – Operator Algebras

Scientific paper

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27 pages, J. Operator Theory (to appear)

Scientific paper

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.

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