- #1
DavideGenoa
- 155
- 5
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
##\infty## thanks!
##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 how to do so. Could anybody help me in finding its (continuous) spectrum, i.e. the set ##\sigma(A)=\{\lambda\in\mathbb{C}\quad|\quad\nexists B\in\mathscr{L}(\ell_2,\ell_2):B=(A-\lambda I)^{-1}\}##?
##\infty## thanks!