Geodesic
Estimates of the distances between sums of the spaces $\ell^p_n$,~II
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 31, Tome 303 (2003), pp. 203-217

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We study classical, modified, and weak Banach–Mazur distances between sums of $\ell^p_n$ spaces. We calculate explicitly the classical and weak Banach–Mazur distances between sums of $\ell^p_n$-spaces and establish bounds for the ratios of these distances between sums of $\ell^p_n$-spaces. 
@article{ZNSL_2003_303_a10,
     author = {A. I. Khrabrov},
     title = {Estimates of the distances between sums of the spaces $\ell^p_n${,~II}},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {203--217},
     publisher = {mathdoc},
     volume = {303},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2003_303_a10/}
}
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A. I. Khrabrov. Estimates of the distances between sums of the spaces $\ell^p_n$,~II. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 31, Tome 303 (2003), pp. 203-217. http://geodesic.mathdoc.fr/item/ZNSL_2003_303_a10/