  We introduce a new set of noncommutative space-time commutation relations in
two space dimensions. The space-space commutation relations are deformations of
the standard flat noncommutative space-time relations taken here to have
position dependent structure constants. Some of the new variables are
non-Hermitian in the most natural choice. We construct their Hermitian
counterparts by means of a Dyson map, which also serves to introduce a new
metric operator. We propose PTlike symmetries, i.e.antilinear involutory maps,
respected by these deformations. We compute minimal lengths and momenta arising
in this space from generalized versions of Heisenberg's uncertainty relations
and find that any object in this two dimensional space is string like,
i.e.having a fundamental length in one direction beyond which a resolution is
impossible. Subsequently we formulate and partly solve some simple models in
these new variables, the free particle, its PT-symmetric deformations and the
harmonic oscillator.
