A projector with different dimensions associated with each quantum number: the dimension information passed to Projector is automatically tracked in the Setup for later use.
A projector where some of the quantum numbers are associated with discrete spaces, and others with continuous spaces (note that you do not need to specify the dimensions again).
When projecting onto a subspace, use the optional argument subspace to avoid having the dimension information tracked in the Setup.
To project the Ket into a basis, take the scalar product of the Projector and the Ket.
Set a bracket rule for, and use the value command to perform the sum (rewrite it explicitly as a sum of terms).