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Geometric Characterizations of Hilbert Spaces
Published online by Cambridge University Press: 20 November 2018
Abstract
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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.
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- Research Article
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- Copyright © Canadian Mathematical Society 2016
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