- #1
mathmajor314
- 9
- 0
Let L be a self-adjoint operator satisfying <Lf,f>=0. Show that [tex]\sigma[/tex](L)[tex]\subseteq[/tex][0,[tex]\infty[/tex]).
I know that L being self-adjoint implies that <Lf,f>=<[tex]\lambda[/tex]f,f>=[tex]\lambda[/tex]<f,f>=[tex]\lambda[/tex]norm(f).
And <Lf,f>=<f,L*f>=<f,Lf>. I'm not sure where to go from here though.
Thank you in advance for any help!
I know that L being self-adjoint implies that <Lf,f>=<[tex]\lambda[/tex]f,f>=[tex]\lambda[/tex]<f,f>=[tex]\lambda[/tex]norm(f).
And <Lf,f>=<f,L*f>=<f,Lf>. I'm not sure where to go from here though.
Thank you in advance for any help!