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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)$.


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

  • [1] T. Figiel, J. Lindenstrauss and V. Milman, The dimension of almost spherical section of convex bodies, Acta Math. 139 (1977), 52-94. (Russian) MR 0445274 (56:3618)
  • [2] V. Gurariĭ, M. Kadec and V. Macaev, On the distance between finite dimensional $ {l_p}$ spaces, Mat. Sb. 70 (1966), 481-489. MR 0196462 (33:4649)
  • [3] N. Tomczak-Jaegermann, The moduli of smoothness and convexity and the Rademacher averages of trace classes $ {S_p}$, Studia Math. 50 (1974), 163-182. MR 0355667 (50:8141)

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Additional Information

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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