suppose X is a banach space and X* be its dual. suppose X* is separable and
f_n be a countable subset of it. by definition we can find unit vector x_n
in X such that |fn(x_n)|>1/2|f_n|.
show that span{x_n} is dense in X.
s*******n 发帖数: 740
2
{f_n}是dense in X*吗？
s*******n 发帖数: 740
3
我估计是漏了f_n dense，要不然f_n全部取相等的肯定不成立
p*****n 发帖数: 758
4
yeah...sorry.. anyway i solved it already.
Still a good problem as a practise. X* separable implies X separable.
