The Banach-Mazur distance between the trace classes $c^{n}_{p}$
HTML articles powered by AMS MathViewer
- by Nicole Tomczak-Jaegermann
- Proc. Amer. Math. Soc. 72 (1978), 305-308
- DOI: https://doi.org/10.1090/S0002-9939-1978-0507329-5
- PDF | Request permission
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
- T. Figiel, J. Lindenstrauss, and V. D. Milman, The dimension of almost spherical sections of convex bodies, Acta Math. 139 (1977), no. 1-2, 53–94. MR 445274, DOI 10.1007/BF02392234
- V. I. Gurariĭ, M. Ĭ. Kadec′, and V. I. Macaev, Distances between finite-dimensional analogs of the $L_{p}$-spaces, Mat. Sb. (N.S.) 70 (112) (1966), 481–489 (Russian). MR 0196462
- Nicole Tomczak-Jaegermann, The moduli of smoothness and convexity and the Rademacher averages of trace classes $S_{p}(1\leq p<\infty )$, Studia Math. 50 (1974), 163–182. MR 355667
Bibliographic Information
- © Copyright 1978 American Mathematical Society
- 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