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Results tagged with banach-spaces
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user 60517
A Banach space is a complete normed vector space: A vector space equipped with a norm such that every Cauchy sequence converges.
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Is $L(\ell_2,\ell_2)$ dense in $L(\ell_2,c_0)$?
Let $\ell_2:=\{ x:\mathbb{N} \to \mathbb{R}: \sum_{j=1}^\infty x_j^2<\infty\}$ and
$c_0:=\{ x:\mathbb{N} \to \mathbb{R}: \lim_{j\to\infty}x_j=0,\, \sup_{j\in\mathbb{N}}|x_j|<\infty\}$ denote the usual …