Geodesic
Paths between Banach spaces
Glasgow mathematical journal, Tome 44 (2002) no. 2, pp. 261-273

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DOI

The Kadets path distance between Banach spaces X and Y is defined to be the infimum of the lengths with respect to the Kadets distance of all curves joining X and Y. If there is no curve joining X and Y, the Kadets path distance between X and Y is defined to be infty .Some approaches to estimates of the Kadets path distance from above and from below are developed. In particular, the Kadets path distances between the spaces l_p^n,\ p\in [1,+\rm (inf)ty ], n\in {\b (N)} are estimated. 
Ostrovskii, M. I. Paths between Banach spaces. Glasgow mathematical journal, Tome 44 (2002) no. 2, pp. 261-273. doi: 10.1017/S0017089502020074
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     title = {Paths between {Banach} spaces},
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     year = {2002},
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     doi = {10.1017/S0017089502020074},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089502020074/}
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