  We consider the problem of quantization of the bosonic membrane via the large
$N$ limit of its matrix regularizations $H_N$ in Fock space. We prove that
there exists a choice of the Fock space frequency such that $ H_N$ can be
written as a sum of a non-interacting Hamiltonian $H_{0,N}$ and the original
normal ordered quartic potential. Using this decomposition we obtain upper and
lower bounds for the ground state energy in the planar limit, we study a
perturbative expansion about the spectrum of $H_{0,N}$, and show that the
spectral gap remains finite at $N=\infty$ at least up to the second order. We
also apply the method to the $U(N)$-invariant anharmonic oscillator, and
demonstrate that our bounds agree with the exact result of Brezin et al.
