Thread: strong topology

Hi all,
i have in my lecture notes this statement :
" the strong topology is equivalent to the topology given by the norm ||w||=sup |(w|v)|
which makes the E' (dual of E ) a Banach space , and the space E is the subspace of E''
"

why the strong topology is equal to this norm topology ?
and why the space E is the subspace of E'' ?

is not "really" a subspace of . It is the case after an identification. We define by the following way. Let defined by . and makes linear.

thanks , i dont get u mean , is it possible to clrify more ?

is a subspace of . We identify with a subspace of .

thanks, but when i see my lecture notes again i saw same experssion that :
" because A is a subspace of A'' ,the elements a belongs to the A can be viewed as functions on X(A) ( characters of A ) by setting :
a(x):=X(a)
"
and still i am confusing about the double dual , how space is the subspace og that , and also i can't understand the meaninig of this phrase that i wrote .