Geodesic
``Suns'' and geometric properties of the unit sphere in a~Banach space
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 5 (1998), pp. 247-253

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In a Banach space, even such simple objects as two-point sets have approximative properties greatly depending on the geometric structure of its unit sphere. A characterization of spcices (abstract and some concrete – $C(Q)$, $G(Q)*$, $L^1(\mu)$ and $L^{\infty}(\mu))$ is given in which every two-point set is an $\alpha$-sun (or a $\gamma$-sun). 
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     author = {L. P. Vlasov},
     title = {``Suns'' and geometric properties of the unit sphere in {a~Banach} space},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {247--253},
     publisher = {mathdoc},
     volume = {5},
     year = {1998},
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     url = {http://geodesic.mathdoc.fr/item/TIMM_1998_5_a17/}
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L. P. Vlasov. ``Suns'' and geometric properties of the unit sphere in a~Banach space. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 5 (1998), pp. 247-253. http://geodesic.mathdoc.fr/item/TIMM_1998_5_a17/