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
As a consequence of Parseval's identity, if is an orthonormal basis of , then the map defined by is an isometric isomorphism of Hilbert spaces: it is a bijective linear mapping such that
for all . The cardinal number of is the Hilbert dimension of . Thus every Hilbert space is isometrically isomorphic to a sequence space for some set .