We consider a non self-adjoint Laplacian on a directed graph with non symmetric weights on edges. We give a criterion for the m-accretiveness and the m-sectoriality of this Laplacian. Our results are based on a comparison of this operator with its symmetric part for which we can apply dierent results concerning essential self-adjointness of a symmetric Laplace operator on an innite graph. This gives results on the heat operator related to our non-symmetric Laplacian.

中文翻译：

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非对称图上的 m-增积拉普拉斯算子

我们在边上具有非对称权重的有向图上考虑非自伴随拉普拉斯算子。我们给出了这个拉普拉斯算子的 m-accretiveness 和 m-部门性的标准。我们的结果是基于这个算子与其对称部分的比较，我们可以应用关于无限图上对称拉普拉斯算子的基本自伴随性的不同结果。这给出了与我们的非对称拉普拉斯算子相关的热算子的结果。