An estimate of distances between finite dimensional symmetric spaces
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part IX, Tome 92 (1979), pp. 268-273
E. D. Gluskin. An estimate of distances between finite dimensional symmetric spaces. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part IX, Tome 92 (1979), pp. 268-273. http://geodesic.mathdoc.fr/item/ZNSL_1979_92_a18/
@article{ZNSL_1979_92_a18,
     author = {E. D. Gluskin},
     title = {An estimate of distances between finite dimensional symmetric spaces},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {268--273},
     year = {1979},
     volume = {92},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1979_92_a18/}
}
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If $E_1$, $E_2$ are two $n$-dimensional symmetric spaces then the Banach–Mazur distance between them satisfies the inequality $d(E_1,E_2)\le cn^{1/2}\log^4n$, where $C$ is an absolute constant.