Conformal field theory
The Hilbert space of physical states is a unitary module of the Virasoro algebra corresponding to a fixed value of "c". Stability requires that the energy spectrum of the Hamiltonian be nonnegative. The modules of interest are the highest weight modules of the Virasoro algebra.
Hilbert space
Unbounded operators are also tractable in Hilbert spaces, and have important applications to quantum mechanics. An unbounded operator on a Hilbert space is defined as a linear operator whose domain is a linear subspace of . Often the domain is a dense subspace of , in which case is known as a densely defined operator.