# Re: Supspaces versus Projectors in QM foundations

**From:** Arnold Neumaier (*Arnold.Neumaier_at_univie.ac.at*)

**Date:** 12/03/04

**Next message:**Arnold Neumaier: "Re: use of real numbers in mathematics and physics"**Previous message:**Arnold Neumaier: "Re: Connes & Marcolli paper on renormalization"**In reply to:**Pierre Asselin: "Re: Supspaces versus Projectors in QM foundations"**Next in thread:**seratend: "Re: Supspaces versus Projectors in QM foundations"**Messages sorted by:**[ date ] [ thread ]

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

**Next message:**Arnold Neumaier: "Re: use of real numbers in mathematics and physics"**Previous message:**Arnold Neumaier: "Re: Connes & Marcolli paper on renormalization"**In reply to:**Pierre Asselin: "Re: Supspaces versus Projectors in QM foundations"**Next in thread:**seratend: "Re: Supspaces versus Projectors in QM foundations"**Messages sorted by:**[ date ] [ thread ]