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On the transpose map of matrix algebras


Author: Jun Tomiyama
Journal: Proc. Amer. Math. Soc. 88 (1983), 635-638
MSC: Primary 46L05; Secondary 16A42
DOI: https://doi.org/10.1090/S0002-9939-1983-0702290-4
MathSciNet review: 702290
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Abstract: It is shown that for the transpose map $ \theta (n)$ of the $ n \times n$ matrix algebra $ {M_n}$, its $ k$ th multiplicity map $ \theta {(n)_k}$ has exactly the norm $ k$ if $ k \leqslant n$, hence the completely bounded norm of $ \theta (n)$ written $ {\left\Vert {\theta (n)} \right\Vert _{cb}}$ equals $ n$. Some applications and related results are also proved.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1983-0702290-4
Keywords: Completely bounded map, $ {C^*}$-algebra, matrix algebra
Article copyright: © Copyright 1983 American Mathematical Society

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