What Does the Notation l.l Represent in Norm Contexts?

[gauss mouse]

If you look here http://planetmath.org/encyclopedia/RiezsLemma.html , there seems to be something missing - nothing is said about the norm of (x_alpha) or about the norm of (s - x_alpha).

Now, the same thing seems to happen here http://planetmath.org/encyclopedia/CompactnessOfClosedUnitBallInNormedSpaces.html , so I guess there's something about the notation that I'm not getting, rather than there being something actually missing.

Can anyone help? To be honest, I fail to see how "lx_alphal and ls-x_alphal for every s in S" could be a statement.

NB: The notation l.l is used to denote norm on the quoted webpages, rather than the more usual ll.ll

 

[Trevor Vadas]

(Riesz Lemma). Fix 0 < $\alpha$ < 1. If S$\subset$ E is a proper closed subspace of a
Banach space E then one can find x$_{\alpha}$ $\in$ X with ||x$_{\alpha}$|| = 1 and |s - x| $\geq$  $\alpha$, for all s $\in$ S