  We study the quantization of compact space on the basis of the Moyal
quantization. We first construct the $su(2)$ algebra that are the functions of
canonical coordinates $a$ and $a^*$. We make use of them to define the adjoint
operators, which is used to define the fuzzy sphere and constitute the algebra.
We show that the vacuum is constructed as the powers of $a^*$, in contrast to
the flat case where the vacuum is defined by the exponential function of $a$
and $a^*$. We present how the analogy of the creation operator acting on the
vacuum is obtaied. The construction does not resort to the ordinary creation
and annihilation operators.
