It may sound as a dumb question but I just want to be sure that I understand all the terminology:
The eigenspaces corresponding to a (non-degenerate) eigenvalue of a operator on a Hilbert space are one-dimensional subspaces. Are they therefore elements of the projective Hilbert space, i.e. rays?
Thank you.
Yes, the elements of a projective Hilbert space are precisely the one-dimensional subspaces of a linear Hilbert space. The term ray appears to be common in the projective space literature, though some people might associate this word with half-line in a real space. Calling them lines or complex lines would be better, in my opinion.