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crysis 2 english.pak download
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crysis 2 english language pack
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On the existence of a non-trivial positive operator which commutes with the forward shift operator
Let $H$ be a complex Hilbert space, $T$ be a closed densely defined linear operator on $H$ and $S$ be the forward shift operator on $H$. I have to show that if $T$ is non-trivial self-adjoint operator then there exists $x\in H$ such that $Tx=Sx$.
I need some suggestion for the solution.
A:
Since $S$ is the forward shift operator, $TS = ST$, and the only closed densely defined operators that commute with $ST$ are multiples of the identity.
If $T$ is a non-trivial self-adjoint operator on $H$, then $T$ is invertible. By Cramer's Rule we have that
$$
T^{ -1} = \frac{1}{\det T
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