A. I. Khrabrov, “Generalized Volume Ratios and the Banach–Mazur Distance”, Mat. Zametki, 70:6 (2001), 918–926; Math. Notes, 70:6 (2001), 838

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Matematicheskie Zametki, 2001, Volume 70, Issue 6, Pages 918–926
DOI: https://doi.org/10.4213/mzm803 (Mi mzm803)

This article is cited in 7 scientific papers (total in 7 papers)

Generalized Volume Ratios and the Banach–Mazur Distance

A. I. Khrabrov

St. Petersburg State University, Department of Mathematics and Mechanics

Full-text PDF (232 kB) Citations (7)

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DOI: https://doi.org/10.4213/mzm803

Abstract: The classical and modified Banach–Mazur distances are studied. A relation between the modified distance and the volume ratios is established. The volume ratios are calculated for the spaces

ℓ_{n}^{p}

$\ell _n^p$ and their sums are estimated for arbitrary finite-dimensional spaces.

Received: 28.06.2000
Revised: 20.01.2001

English version:
Mathematical Notes, 2001, Volume 70, Issue 6, Pages 838–846
DOI: https://doi.org/10.1023/A:1012920103463

Bibliographic databases:

UDC: 513.881

Language: Russian

Citation: A. I. Khrabrov, “Generalized Volume Ratios and the Banach–Mazur Distance”, Mat. Zametki, 70:6 (2001), 918–926; Math. Notes, 70:6 (2001), 838–846

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/mzm803

https://doi.org/10.4213/mzm803

https://www.mathnet.ru/eng/mzm/v70/i6/p918

This publication is cited in the following 7 articles:

Galicer D., Merzbacher M., Pinasco D., “Asymptotic Estimates For the Largest Volume Ratio of a Convex Body”, Rev. Mat. Iberoam., 37:6 (2021), 2347–2372
A. I. Khrabrov, “Volume ratio for the Cartesian product of convex bodies”, St. Petersburg Math. J., 32:5 (2021), 905–916
F. L. Bakharev, “Generalization of some classical results to the case of the modified Banach–Mazur distance”, J. Math. Sci. (N. Y.), 141:5 (2007), 1517–1525
Averkov, G, “On the inequality for volume and Minkowskian thickness”, Canadian Mathematical Bulletin-Bulletin Canadien de Mathematiques, 49:2 (2006), 185
A. I. Khrabrov, “Comparison of Some Distances Between Sums of $\ell^{p}_n$ Spaces”, Funct. Anal. Appl., 38:1 (2004), 75–77
Gordon, Y, “John's decomposition in the general case and applications”, Journal of Differential Geometry, 68:1 (2004), 99
A. I. Khrabrov, “Estimates of the distances between sums of the spaces $\ell^p_n$ , II”, J. Math. Sci. (N. Y.), 129:4 (2005), 4040–4048

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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Full-text PDF :	378
References:	88
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