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47b47 (primary)

Journal of the London Mathematical Society (1)

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ON THE NORM OF ELEMENTARY OPERATORS
A. BLANCO, M. BOUMAZGOUR, T. J. RANSFORD
Journal:

Journal of the London Mathematical Society / Volume 70 / Issue 2 / October 2004

Published online by Cambridge University Press:

01 October 2004, pp. 479-498

Print publication:

October 2004
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The norm problem is considered for elementary operators of the form $U_{a,b}\,{:}\,{\cal A}\,{\longrightarrow}\,{\cal A},\;x\longmapsto axb\,{+}\,bxa (a,\,b\,{\in}\,{\cal A})$ in the special case when ${\cal A}$ is a subalgebra of the algebra of bounded operators on a Banach space. In particular, the lower estimate $\|U_{a,b}\|\geq\|a\|\|b\|$ is established when the Banach space is a Hilbert space and ${\cal A}$ is the algebra of all bounded linear operators.