Riesz’ Lemma

Let $E$ be a normed space, $S\subset E$ a closed proper vector subspace, and . Then there is $x_{\alpha }\in E\setminus S$ such that $\parallel x_{\alpha }\parallel =1$ and $\parallel s-x_{\alpha }\parallel >\alpha$ for every $s\in S$.

Title	Riesz’ Lemma
Canonical name	RieszLemma
Date of creation	2013-03-22 14:56:11
Last modified on	2013-03-22 14:56:11
Owner	gumau (3545)
Last modified by	gumau (3545)
Numerical id	6
Author	gumau (3545)
Entry type	Theorem
Classification	msc 15A03
Classification	msc 54E35