After a short introduction where a few main notions and results are recalled, we state some results connected with generated and L_∞-type pseudoresolvents. Among others, we give theorems of characterization both for L_∞-type pseudoresolvents and for their generators. The relation between L_∞-type pseudoresolvents and C₀-equicontinuous semigroups is also pointed out. The last part of the present paper is devoted to approximation of pseudoresolvents and their generators. If \(R_{n}, R : \Lambda \rightarrow L(X), n \geq 1\) are generated pseudoresolvents and A _n , A their generators, we investigate conditions under which A is approximated by A _n and R is approximated by R _n , n ≥ 1. In addition, we give conditions under which a sequence of generated pseudoresolvents approximates a pseudoresolvent, and in this case we study the connection between generators.

中文翻译：

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伪溶剂的近似值

一个简短的介绍，其中一些主要的概念和结果召回后，我们国家有产生并连接了一定的成效大号_∞型pseudoresolvents。其中，我们既提供了表征定理大号_∞型pseudoresolvents并为他们的发电机。之间的关系大号_∞型pseudoresolvents和Ç ₀ -equicontinuous半群也指出。本文的最后一部分致力于伪溶剂及其生成器的近似。如果生成\（R_ {n}，R：\ Lambda \ rightarrow L（X），n \ geq 1 \），则伪生成A _n，A 他们的发电机，我们研究在其下是由近似条件甲_Ñ和- [R近似为[R _Ñ，Ñ  ≥1中。另外，我们给根据该生成pseudoresolvents序列近似于pseudoresolvent条件，并且在这种情况下，我们研究了发电机之间的连接。