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The Banach-Mazur distance between the trace classes $ c\sp{n}\sb{p}$


Author: Nicole Tomczak-Jaegermann
Journal: Proc. Amer. Math. Soc. 72 (1978), 305-308
MSC: Primary 46B20
DOI: https://doi.org/10.1090/S0002-9939-1978-0507329-5
MathSciNet review: 507329
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Abstract: The Banach-Mazur distance between $ l_2^n\hat \otimes l_2^m$ and $ l_2^n\hat \hat \otimes l_2^m$ is shown to be of the order $ \sqrt {\min (n,m)} $. Our proof yields that the distance between the trace classes $ c_p^n$ and $ c_q^n$ is of the same order as $ d(l_p^n,l_q^n)$.


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DOI: https://doi.org/10.1090/S0002-9939-1978-0507329-5
Keywords: Banach-Mazur distance, trace class, tensor products, cross norms
Article copyright: © Copyright 1978 American Mathematical Society

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