Bi-continuous semigroups on sequentially complete random Saks spaces

Leilei Wei; Xia Zhang; Ming Liu; Leilei Wei; Xia Zhang; Ming Liu

doi:10.3934/era.2025250

Electronic Research Archive

2025, Volume 33, Issue 9: 5616-5637. doi: 10.3934/era.2025250

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Research article

Bi-continuous semigroups on sequentially complete random Saks spaces

School of Mathematical Sciences, TianGong University, Tianjin 300387, China

Received: 06 June 2025 Revised: 15 July 2025 Accepted: 01 August 2025 Published: 17 September 2025

In this paper, we first introduced the Riemann integral for an abstract-valued function from a finite closed real interval to a sequentially complete random Saks space and gave the fundamental theorem of calculus for an $ L^{0} $-Lipschitz function. Then we investigated some important properties peculiar to bi-continuous semigroups on a sequentially complete random Saks space. Finally, based on the above work, we established the Hille-Yosida generation theorem for such bi-continuous semigroups, which extends and improves several known results.
- random Saks spaces,
- bi-continuous semigroups,
- Hille-Yosida generation theorem,
- $ (\varepsilon, \lambda) $-topology
Citation: Leilei Wei, Xia Zhang, Ming Liu. Bi-continuous semigroups on sequentially complete random Saks spaces[J]. Electronic Research Archive, 2025, 33(9): 5616-5637. doi: 10.3934/era.2025250

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Abstract

In this paper, we first introduced the Riemann integral for an abstract-valued function from a finite closed real interval to a sequentially complete random Saks space and gave the fundamental theorem of calculus for an $ L^{0} $-Lipschitz function. Then we investigated some important properties peculiar to bi-continuous semigroups on a sequentially complete random Saks space. Finally, based on the above work, we established the Hille-Yosida generation theorem for such bi-continuous semigroups, which extends and improves several known results.

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