Recent content by Leitmotif

  1. L

    Showing that spectrum of operator is not compact

    Point taken. Thanks for the input :)
  2. L

    Showing that spectrum of operator is not compact

    Well, I guess I came up with an example of a function that's in the domain, and whose set of eigenvalues are not bounded, and eigenvalues are in the spectrum. I just wasn't really sure if that is enough to show that it's true for ALL functions in the domain. Also, I noticed I made a mistake...
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    Showing that spectrum of operator is not compact

    Yikes, the preview looked fine, but not sure what happened with that LaTeX code there. The operator is second derivative, Tx=x", and the domain is all functions in X so that x(0)=x(Pi)=0.
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    Showing that spectrum of operator is not compact

    Homework Statement Let X=C[0,\pi]. Define T:\mathcal{D}(T) \to X, Tx = x" where \mathcal{D}(T) = \{ x \in X | x(0)=x(\pi)=0 \}. Show that \sigma(T) is not compact. Homework Equations None. The Attempt at a Solution Well, functions sin(Ax) and sin(-Ax), for A=0,1,2,... are in the domain...