The Russo-Dye Theorem in a weakly closed 𝒯(𝒩)–module

Dong, Zhe

doi:10.1090/S0002-9939-04-07141-2

The Russo-Dye Theorem in a weakly closed $\mathcal {T(N)}$–module
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by Zhe Dong

Proc. Amer. Math. Soc. 132 (2004), 2257-2263

DOI: https://doi.org/10.1090/S0002-9939-04-07141-2

Published electronically: March 25, 2004

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Abstract:

Suppose that $\mathcal {N}$ is admissible. It is shown that the convex hull of unitary elements of a weakly closed $\mathcal {T(N)}$–module $\mathcal {U}$ contains the whole unit ball of $\mathcal {U}$ if and only if $\widetilde {I}=I$ and for any $N>0$, $\widetilde N>0$.

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