标题： 适当耗散扩展的对偶对 显示英文标题

标题： The Proper Dissipative Extensions of a Dual Pair

摘要： 设$A$和$(-\widetilde{A})$是希尔伯特空间$\mathcal{H}$上的耗散算子，并且$(A,\widetilde{A})$形成一对对偶，即$A\subset\widetilde{A}^*$，分别地$\widetilde{A}\subset A^*$。我们提出一种确定该对偶对的适当耗散扩张$\widehat{A}$的方法，即 $A\subset \widehat{A}\subset\widetilde{A}^*$在$\mathcal{D}(A)\cap\mathcal{D}(\widetilde{A})$在$\mathcal{H}$中稠密的条件下提供。对对称算子、由相对有界耗散算子扰动的对称算子以及更奇异的微分算子的应用进行了讨论。最后，我们研究了不同耗散扩张的数值范围的稳定性。 显示英文摘要

摘要： Let $A$ and $(-\widetilde{A})$ be dissipative operators on a Hilbert space $\mathcal{H}$ and let $(A,\widetilde{A})$ form a dual pair, i.e. $A\subset\widetilde{A}^*$, resp.\ $\widetilde{A}\subset A^*$. We present a method of determining the proper dissipative extensions $\widehat{A}$ of this dual pair, i.e. $A\subset \widehat{A}\subset\widetilde{A}^*$ provided that $\mathcal{D}(A)\cap\mathcal{D}(\widetilde{A})$ is dense in $\mathcal{H}$. Applications to symmetric operators, symmetric operators perturbed by a relatively bounded dissipative operator and more singular differential operators are discussed. Finally, we investigate the stability of the numerical range of the different dissipative extensions.