论文标题
具有近距离假想部分的耗散操作员的扩展
Extensions of dissipative operators with closable imaginary part
论文作者
论文摘要
给定复杂的Hilbert Space $ \ Mathcal {H} $上的耗散操作员$ a $，以便使二次形式$ f \ mapsto \ mbox {im} \ langle f，af \ rangle $是可近的，我们为扩展$ a $ dissuptions dissipative提供了必要和足够的条件。作为应用程序，我们描述了严格阳性对称操作员的所有最大增强性扩展以及在间隔上高度奇异的一阶操作员的所有最大耗散扩展。
Given a dissipative operator $A$ on a complex Hilbert space $\mathcal{H}$ such that the quadratic form $f\mapsto \mbox{Im}\langle f,Af\rangle$ is closable, we give a necessary and sufficient condition for an extension of $A$ to still be dissipative. As applications, we describe all maximally accretive extensions of strictly positive symmetric operators and all maximally dissipative extensions of a highly singular first-order operator on the interval.
