Computing the norms of elementary operators
Timoney, Richard M.
Illinois J. Math., Tome 47 (2003) no. 4, p. 1207-1226 / Harvested from Project Euclid
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We provide a direct proof that the Haagerup estimate on the completely bounded norm of elementary operators is best possible in the case of $\mathcal{B}(H)$ via a generalisation of a theorem of Stampfli. We show that for an elementary operator $T$ of length $\ell$, the completely bounded norm is equal to the $k$-norm for $k = \ell$. A $C$*-algebra $A$ has the property that the completely bounded norm of every elementary operator is the $k$-norm, if and only if $A$ is either $k$-subhomogeneous or a $k$-subhomogeneous extension of an antiliminal $C$*-algebra.
Publié le : 2003-10-15
Classification:  47B47,  46L07,  47A12,  47A30,  47L25 
@article{1258138100,
     author = {Timoney, Richard M.},
     title = {Computing the norms of elementary operators},
     journal = {Illinois J. Math.},
     volume = {47},
     number = {4},
     year = {2003},
     pages = { 1207-1226},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1258138100}
}

Timoney, Richard M. Computing the norms of elementary operators. Illinois J. Math., Tome 47 (2003) no. 4, pp.  1207-1226. http://gdmltest.u-ga.fr/item/1258138100/