  We study deformation quantization on an infinite-dimensional Hilbert space
$W$ endowed with its canonical Poisson structure. The standard example of the
Moyal star-product is made explicit and it is shown that it is well defined on
a subalgebra of $C^\infty(W)$. A classification of inequivalent deformation
quantizations of exponential type, containing the Moyal and normal
star-products, is also given.
