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


Author: Zhe Dong
Journal: Proc. Amer. Math. Soc. 132 (2004), 2257-2263
MSC (2000): Primary 47L75
Published electronically: March 25, 2004
MathSciNet review: 2052401
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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: https://doi.org/10.1090/S0002-9939-04-07141-2
Keywords: Russo-Dye Theorem, weakly closed $\mathcal{T(N)} $--module, unitary operator
Received by editor(s): October 19, 2000
Published electronically: March 25, 2004
Communicated by: David R. Larson
Article copyright: © Copyright 2004 American Mathematical Society