Dear friends, I would like to find the spectrum of the linear operator ##A\in\mathscr{L}(\ell_2,\ell_2)##, which I have verified to be compact and eigenvalueless, defined by
##A(x_1,x_2,x_3,...,x_n,...)=(0,x_1,\frac{1}{2}x_2,...,\frac{1}{n-1}x_{n-1},...)##
but my book does not give examples of...