An example of an unbounded non-orthogonal projection in a Hilbert space What is an example of an unbounded non-orthogonal projection in a Hilbert spaces? 
Does it exist?
A non-orthogonal projection is an idempotent operator: $T^2=T$. So the question is: can such an operator be unbounded? 

If $\phi$ is an unbounded linear functional, take $u$ so that $\phi(u) = 1$,
and define $P x = \phi(x) u$.
You won't get an explicit example though, because the existence of an unbounded linear operator on an infinite-dimensional Hilbert space requires some form of the Axiom of Choice.
