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## Homework Statement

Let [tex]X=C[0,\pi][/tex].

Define [tex]T:\mathcal{D}(T) \to X[/tex], Tx = x" where

[tex]\mathcal{D}(T) = \{ x \in X | x(0)=x(\pi)=0 \}[/tex].

Show that [tex]\sigma(T)[/tex] 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, and eigenvalues are all integers, which are not bounded, aka. not compact. But I am not sure how to show this in general case. Any help in the right direction is appreciated.

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