Open Access
Original Articles
(σ,γ)- Generalized Dynamics on Modules
M. Mosadeqmosadeq@mshdiau.ac.irDepartment of MathematicsFaculty of SciencesIslamic Azad UniversityMashhad Branch, Mashhad, IranView full profile → , M. Hassanihassani@mshdiau.ac.irDepartment of MathematicsFaculty of SciencesIslamic Azad UniversityMashhad Branch, Mashhad, IranView full profile → , A. Niknamdassamankin@yahoo.co.ukDepartment of Mathematics andCenter of Excelence in Analysis on Algebraic Structures(Ceaas)Ferdowsi UniversityMashhad, IranView full profile →
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- Published Online:
- 03 Jun 2013
- Article type:
- Original Articles
- Language:
- EN
- Article no.:
- 1726037X.2011.10698600
- Pages:
- 171–184
Abstract
In this paper we introduce the notions of generalized d – derivations, (σ,γ) – generalized module maps and (σ,γ) – generalized dynamics on Modules. We show that if φ : R → B(M) is a σ – dynamics on Banach algebra A with the infinitesimal generator d and T : R → B(M) is a (σ, γ) – generalized dynamics on Banach A – bimodule M with the infinitesimal generator δ, then δ is a generalized d – derivation. Using the computation formula for δn(ax) and the concept of γ– one parameter groups on M, we prove the converse under some more restrictions on δ.
Keywords
References
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