Asymptotically non-expansive actions of strongly amenable semigroups and fixed points
| Autor: | Rasoul Nasr-Isfahani, Abdolmohammad Aminpour, Ayatollah Dianatifar |
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| Rok vydání: | 2018 |
| Předmět: |
Pure mathematics
Mathematics::Operator Algebras Group (mathematics) Semigroup Applied Mathematics Open problem 010102 general mathematics Regular polygon Banach space Fixed point Space (mathematics) 01 natural sciences 010101 applied mathematics Ideal (ring theory) 0101 mathematics Analysis Mathematics |
| Zdroj: | Journal of Mathematical Analysis and Applications. 461:364-377 |
| ISSN: | 0022-247X |
| DOI: | 10.1016/j.jmaa.2017.12.061 |
| Popis: | In this paper, we deal with some fixed point properties for a semi-topological semigroup S acting on a compact convex subset K of a Banach space. We first focus on the space L M C ( S ) of left multiplicatively continuous functions on S and its strong left amenability; the existence of a compact left ideal group in the LMC-compactification of S . We then study the relation between left amenability and strong left amenability of L M C ( S ) with a common fixed point property for non-expansive and asymptotically non-expansive actions of S . Our results improve a result of T. Mitchell in 1970, and answer an open problem of A.T.-M. Lau in 2010 for the class of strongly left amenable semi-topological semigroups. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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