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

Author(s): Zhe Dong
Journal: Proc. Amer. Math. Soc. 132 (2004), 2257-2263.
MSC (2000): Primary 47L75
Posted: 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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Additional Information:

Zhe Dong
Affiliation: Department of Mathematics, Zhejiang University, Hangzhou 310027, People's Republic of China
Email: dongzhe@zju.edu.cn

DOI: 10.1090/S0002-9939-04-07141-2
PII: S 0002-9939(04)07141-2
Keywords: Russo-Dye Theorem, weakly closed $\mathcal{T(N)} $--module, unitary operator
Received by editor(s): October 19, 2000
Posted: March 25, 2004
Communicated by: David R. Larson
Copyright of article: Copyright 2004, American Mathematical Society

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