A note on the Lumer–Phillips theorem for bi-continuous semigroups

IF 0.7 3区数学 Q2 MATHEMATICS

Zeitschrift fur Analysis und ihre Anwendungen Pub Date : 2022-06-02 DOI:10.4171/ZAA/1709

K. Kruse, C. Seifert

引用次数: 5

Abstract

Given a Banach space $X$ and an additional coarser Hausdorff locally convex topology $\tau$ on $X$ we characterise the generators of $\tau$-bi-continuous semigroups in the spirit of the Lumer--Phillips theorem, i.e. by means of dissipativity w.r.t.~a directed system of seminorms and a range condition.

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双连续半群的Lumer-Phillips定理的注解

给定Banach空间$X$和$X$上的另一个粗Hausdorff局部凸拓扑$\tau$，我们根据Lumer-Phillips定理的精神，即通过耗散w.r.t.~半模的有向系统和范围条件，刻画了$\tau$-双连续半群的生成元。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Zeitschrift fur Analysis und ihre Anwendungen 数学-数学

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Analysis and its Applications aims at disseminating theoretical knowledge in the field of analysis and, at the same time, cultivating and extending its applications. To this end, it publishes research articles on differential equations and variational problems, functional analysis and operator theory together with their theoretical foundations and their applications – within mathematics, physics and other disciplines of the exact sciences.