Geodesic
Generalized Volume Ratios and the Banach--Mazur Distance
Matematičeskie zametki, Tome 70 (2001) no. 6, pp. 918-926

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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 $\ell _n^p$ and their sums are estimated for arbitrary finite-dimensional spaces. 
@article{MZM_2001_70_6_a9,
     author = {A. I. Khrabrov},
     title = {Generalized {Volume} {Ratios} and the {Banach--Mazur} {Distance}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {918--926},
     publisher = {mathdoc},
     volume = {70},
     number = {6},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2001_70_6_a9/}
}
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A. I. Khrabrov. Generalized Volume Ratios and the Banach--Mazur Distance. Matematičeskie zametki, Tome 70 (2001) no. 6, pp. 918-926. http://geodesic.mathdoc.fr/item/MZM_2001_70_6_a9/