Generation of Relatively Uniformly Continuous Semigroups on Vector Lattices

被引：3

作者：

Kaplin, M. ^{[1
,2
]}

Fijavz, M. Kramar ^{[1
,3
]}

机构：

[1] Inst Math Phys & Mech, Jadranska 19, SI-1000 Ljubljana, Slovenia

[2] Univ Ljubljana, Fac Math & Phys, Jadranska 19, SI-1000 Ljubljana, Slovenia

[3] Univ Ljubljana, Fac Civil & Geodet Engn, Jamova Cesta 2, Ljubljana, Slovenia

来源：

ANALYSIS MATHEMATICA | 2020年 / 46卷 / 02期

关键词：

vector lattice; positive operator semigroup; relative uniform convergence; generator; Hille-Yosida theorem;

D O I：

10.1007/s10476-020-0025-y

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove a Hille-Yosida type theorem for relatively uniformly continuous positive semigroups on vector lattices. We introduce the notions of relatively uniformly continuous, differentiable, and integrable functions on Double-struck capital R+. These notions allow us to study the generators of relatively uniformly continuous semigroups. Our main result provides sufficient and necessary conditions for an operator to be the generator of an exponentially order bounded, relatively uniformly continuous, positive semigroup.

引用

页码：293 / 322

页数：30

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