Journal of Dynamical Systems and Geometric Theories, Volume (9), No (2), Year (2011-1) , Pages (171-184)

Title : ( σ, γ− Generalized Dynamics on Modules )

Authors: M. Mosadeq , M. Hassani , Asadollah Niknam ,

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Abstract

Abstract. In this paper we introduce the notions of generalized d− derivations, (, )− generalized module maps and (, )− generalized dynamics on Modules. We show that if \\\' : R ! B(M) is a − dynamics on Banach algebra A with the infinitesimal generator d and T : R ! B(M) is a (, )− generalized dynamics on Banach A− bimodule M with the infinitesimal generator , then  is a generalized d− derivation. Using the computation formula for n(ax) and the concept of − one parameter groups on M, we prove the converse under some more restrictions on .

Keywords

, (inner) generalized d− derivation, (quasi inner) (, )− generalized module map, − one parameter group, (, )− generalized dynamics.