Non-Hermitian Extension of Q Uncertainty Relation

In quantum mechanics it is well known that observables are represented by hermitian matrices (or operators). Uncertainty relations are represented as some kinds of trace inequalities satisfied by two observables and one density matrix (or operator). By releasing the hermitian restriction on observables, we obtained non-hermite uncertainty relations. In this paper we give several non-hermitian extensions of Heisenberg or Schrödinger type q uncertainty relations for generalized skew information under some conditions.