Abstract: In quantum mechanics, the Heisenberg uncertainty relation which has been widely applied in many fields is a very important relation. In the traditional uncertainty, self-adjoint operator is considered. This paper researches the Heisenberg uncertainty relation of the bounded linear operators. Firstly, some relevant concepts about the general bounded linear operators are introduced, then it gets a new Heisenberg uncertainty relation by the theory of operator and matrix. Finally, a further generalization of the Heisenberg uncertainty relation is showed and proved .

Key words: Wigner-Yanase-Dyson skew information, density operator, symmetrized commutator

摘要： 在量子力学中，Heisenberg不确定性关系是一个极为重要的关系式，并在许多领域得到了广泛应用。传统的不确定性都是考虑自伴算子，研究了Hilbert空间上一对有界线性算子的Heisenberg不确定性关系。介绍了关于一般有界线性算子的相关概念，在此基础上运用算子论和矩阵论的方法，给出了广义的Heisenberg不确定性关系的表达式;最后对这个不确定关系的推广给出了证明。

关键词: Wigner-Yanase-Dyson斜信息, 密度算子, 对称交换子