论文标题
Hille-Yosida Generation定理几乎肯定有限制的$ C_ {0} $ - 连续模块同构的半群$^1 $
The Hille-Yosida generation theorem for almost surely bounded $C_{0}$--semigroups of continuous module homomorphisms$^1$
论文作者
论文摘要
在本文中，我们首先研究了$ c_ {0} $的一些属性 - 连续模块同构的半群，并给出了这种$ c_ {0} $的特征 - 几乎可以肯定地有界限。然后，基于这些，我们为几乎肯定有限制的$ c_ {0} $建立了Hille-Yosida Generation定理 - 连续模块同构的半群，这概括了一些已知的结果。此外，本文构建的反例还表明，有必要需要此类$ C_ {0} $的几乎确定的有限性 - Semigroups。
In this paper, we first study some properties peculiar to $C_{0}$--semigroups of continuous module homomorphisms and give a characterization for such a $C_{0}$--semigroup to be almost surely bounded. Then, based on these, we establish the Hille-Yosida generation theorem for almost surely bounded $C_{0}$--semigroups of continuous module homomorphisms, which generalizes some known results. Moreover, the counterexample constructed in this paper also shows that it is necessary to require the almost sure boundedness for such $C_{0}$--semigroups.
