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## Homework Statement

unitary operators on hilbert space

## Homework Equations

is there a unitary operator on a (finite or infinite) Hilbert space so that cU(x)=y, for some

constant (real or complex), where x and y are fixed non-zero elements in H ?

## The Attempt at a Solution

I know the answer in R^2, it is enough to consider U a suitable rotation so that U(x)

be a point on the straight line Ry={ry; r ε R}, and then there is a scaler r in R so that

rU(x)=y. I guess this is true for R^n too.