In mathematical words, an observable is an operator that a set of linearly independent eigenfunctions constitutes a complete basis of the wave-functions' space.
Now, let's consider some observables: $O_i, i \in I$ (ex.: $P^2, L^2, S_z, ...$) and a multi-variable function $f$. Let $O = f(O_i, i \in I)$ (ex.: $O = L.M_S$).
Is $O$ an observable?
I'm interested to the property that a hermitian operator has a complete set of eigenfunctions (that generate the whole wave-space : basis). Some authors (C. C. Tanoudji) call it the observability. Let's just call that property "completeness", to avoid confusion.