In his Quantum Mechanics, Ballentine says that “in general, a self-adjoint operator which obeys $\rho^2=\rho$ is a projection operator”. I'm not sure I follow the need for the self-adjoint caveat? I thought that $\rho^2=\rho$ defined a projection operator? Is there any reason he would add this caveat that I'm missing, perhaps in the application to the weird (rigged Hilbert) spaces in which quantum mechanics is done?
2026-03-27 16:20:16.1774628416
Projection operator (redundant?) definition
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