Re: Supspaces versus Projectors in QM foundations

From: Arnold Neumaier (Arnold.Neumaier_at_univie.ac.at)
Date: 12/03/04


Date: Fri, 3 Dec 2004 22:49:08 +0000 (UTC)

Pierre Asselin wrote:
> seratend <ser_monmail@yahoo.fr> wrote:
>
>>A projector is any *hermitian* operator P that satisfies the relation
>>P^2=P.
>>The hermitian condition is the one that fixes the phase.
>
>
> Ok, I'll bite. Do you have an example of a non-hermitian P
> such that P^2= P ? It would have to be non-normal as well,
> and possibly use infinite dimensionality in a tricky way.
> Finding one would be, like, work. Better to ask :-)

No, better work. You won't learn much without. Try to find a 2x2 example
by specifying one entry and solving the equation P^2=P for the remaining
ones. To save work, fix another entry by assuming that P is singular.

Arnold Neumaier