http://arxiv.org/pdf/math/0205003v1
In around equation (1.1) the author says
"By necessity all authors have been led in one way or another to the natural approximation
$F(n) := \sum_{a=1}^n \mu(a) \rho_a$
which tends to $-\chi$ both a.e. and in L1 norm when restricted to (0,1) but which has been shown to diverge in H."
My question is:
How to determine $F$ diverges in $L^2(0,1)$? because $\int_{0}^{1} |1 + F|^2 dx < \infty$ where $F \to -1$?
I am new to functional analysis, so little confused on this.
Thanks,
Roupam