A Hille-Yosida theorem for bi-continuous semigroups. (English) Zbl 1064.47040
The author introduces the concept of “bi-continuous” one-parameter semigroups of operators on Banach spaces, and then characterizes their generators by generalizing the Hille-Yosida theorem. The obtained result extends a result of J. R. Dorroh and J. W. Neuberger in [J. Funct. Anal. 136, No. 1, 114–126 (1996; Zbl 0848.22005)].
Reviewer: Nguyen Van Minh (Carrollton)
MSC:
47D03 | Groups and semigroups of linear operators |
47D06 | One-parameter semigroups and linear evolution equations |