Sun Dual Theory For Bi-Continuous Semigroups

IF 0.6 3区数学 Q3 MATHEMATICS

Analysis Mathematica Pub Date : 2024-03-28 DOI:10.1007/s10476-024-00014-z

K. Kruse, F.L. Schwenninger

引用次数: 0

Abstract

The sun dual space corresponding to a strongly continuous semigroup is a known concept when dealing with dual semigroups, which are in general only weak \(^*\)-continuous. In this paper we develop a corresponding theory for bi-continuous semigroups under mild assumptions on the involved locally convex topologies. We also discuss sun reflexivity and Favard spaces in this context, extending classical results by van Neerven.

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双连续半群的太阳二元论

与强连续半群对应的太阳对偶空间是处理对偶半群时的一个已知概念，一般来说，对偶半群只有弱（^*\）连续性。在本文中，我们根据对相关局部凸拓扑的温和假设，为双连续半群建立了相应的理论。在此背景下，我们还讨论了太阳反射性和 Favard 空间，扩展了 van Neerven 的经典结果。

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

Analysis Mathematica MATHEMATICS-

CiteScore

1.00

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： Traditionally the emphasis of Analysis Mathematica is classical analysis, including real functions (MSC 2010: 26xx), measure and integration (28xx), functions of a complex variable (30xx), special functions (33xx), sequences, series, summability (40xx), approximations and expansions (41xx). The scope also includes potential theory (31xx), several complex variables and analytic spaces (32xx), harmonic analysis on Euclidean spaces (42xx), abstract harmonic analysis (43xx). The journal willingly considers papers in difference and functional equations (39xx), functional analysis (46xx), operator theory (47xx), analysis on topological groups and metric spaces, matrix analysis, discrete versions of topics in analysis, convex and geometric analysis and the interplay between geometry and analysis.