Geodesic
Geometric Characterizations of Hilbert Spaces
Canadian mathematical bulletin, Tome 59 (2016) no. 4, pp. 769-775

Voir la notice de l'article provenant de la source Cambridge University Press

We study some geometric properties related to the set $${{\Pi }_{X}}\,:=\left\{ \left( x,\,{{x}^{*}} \right)\,\in \,{{\text{S}}_{X}}\,\times \,{{\text{S}}_{{{X}^{*}}}}\,:\,{{x}^{*}}\left( x \right)\,=\,1 \right\}$$ obtaining two characterizations of Hilbert spaces in the category of Banach spaces. We also compute the distance of a generic element $\left( h,\,k \right)\,\in \,H\,{{\oplus }_{2}}\,H$ to ${{\Pi }_{H}}$ for $H$ a Hilbert space.
DOI : 10.4153/CMB-2016-019-8
Mots-clés : 46B20, 46C05, Hilbert space, extreme point, smooth, L2-summands 
García-Pacheco, Francisco Javier; Hill, Justin R. Geometric Characterizations of Hilbert Spaces. Canadian mathematical bulletin, Tome 59 (2016) no. 4, pp. 769-775. doi: 10.4153/CMB-2016-019-8
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     title = {Geometric {Characterizations} of {Hilbert} {Spaces}},
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     doi = {10.4153/CMB-2016-019-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2016-019-8/}
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