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ON THE NORM OF ELEMENTARY OPERATORS

Published online by Cambridge University Press:  01 October 2004

A. BLANCO
Affiliation:
Département de Mathématiques et de Statistique, Université Laval, Québec, Canada G1K 7P4
M. BOUMAZGOUR
Affiliation:
Département de Mathématiques et de Statistique, Université Laval, Québec, Canada G1K 7P4
T. J. RANSFORD
Affiliation:
Département de Mathématiques et de Statistique, Université Laval, Québec, Canada G1K 7P4
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Abstract

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.

Type
Notes and Papers
Copyright
The London Mathematical Society 2004

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