Geodesic
Extremally distant normed spaces with additional restrictions
Matematičeskie zametki, Tome 79 (2006) no. 3, pp. 339-352

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We study the relationship between the Banach—Mazur distance and the modified Banach—Mazur distance. We sharpen the Szarek theorem on the construction of invariant norms with specific properties and construct extremally distant normed spaces with norms invariant under groups of automorphisms of small cardinality. We prove that the trivial upper bound for the Banach—Mazur distance obtained in terms of the modified Banach—Mazur distance is order-sharp. 
@article{MZM_2006_79_3_a1,
     author = {F. L. Bakharev},
     title = {Extremally distant normed spaces with additional restrictions},
     journal = {Matemati\v{c}eskie zametki},
     pages = {339--352},
     publisher = {mathdoc},
     volume = {79},
     number = {3},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2006_79_3_a1/}
}
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F. L. Bakharev. Extremally distant normed spaces with additional restrictions. Matematičeskie zametki, Tome 79 (2006) no. 3, pp. 339-352. http://geodesic.mathdoc.fr/item/MZM_2006_79_3_a1/