论文标题
本质上是强制性形式和不可分割的紧凑型半群
Essentially coercive forms and asympotically compact semigroups
论文作者
论文摘要
形式方法最有效地证明了半群的生成定理，也可以证明自我偶然性。到目前为止，这些定理是基于允许使用宽松的 - 米尔姆格拉姆引理的强制性概念。在这里，我们考虑了更弱的“基本”版本的强制性，这已经足以获得半群或自助式操作员的发电机。我们还表明，这些特性之一，即基本上是正胁迫，意味着S的特殊渐近行为，即渐近紧凑。即，由于t趋向于无穷大，d（s（t），k（h））趋向于0，其中k（h）表示所有紧凑型操作员在基础希尔伯特（Hilbert）空间上的空间。
Form methods are most efficient to prove generation theorems for semigroups but also for proving selfadjointness. So far those theorems are based on a coercivity notion which allows the use of the Lax-Milgram Lemma. Here we consider weaker "essential" versions of coerciveness which already suffice to obtain the generator of a semigroup S or a selfadjoint operator. We also show that one of these properties, namely essentially positive coerciveness implies a very special asymptotic behaviour of S, namely asymptotic compactness; i.e. that dist(S(t),K(H)) tends to 0 as t tends to infinity, where K(H) denotes the space of all compact operators on the underlying Hilbert space.
