C-半群的Lumer-Phillips定理与C-Hermitian算子

Lumer-Phillips Theorem for C-Semigroups and C-Hemitian Operators

本文给出了稠定闭算子A(或A的扩张)生成压缩C-半群的充分条件,且在C是等距算子时,证明了该条件是必要的,推广了Lumer-Phillips定理.并用结果刻划了等距C-群的生成元.

We give a sufficient condition, for a densely defined operator A, generating a contract C-semigroup, which is also necessary if C is a isometric operator, this generalize the Lumer-Phillips theorem; moreover, we use this result to describe the generators of isometric C-semigroups.