Acta mathematica scientia,Series B ›› 2012, Vol. 32 ›› Issue (2): 783-792.doi: 10.1016/S0252-9602(12)60058-7

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APPROXIMATION OF ADJOINT OF A MULTIPLIER ON BANACH ALGEBRAS

A. Ghaffari|S. Javadi|H. Khodaei   

  1. Department of Mathematics, Semnan University, P. O. Box 35195-363, Semnan, Iran
  • Received:2010-01-28 Revised:2010-12-11 Online:2012-03-20 Published:2012-03-20

Abstract:

For a Banach algebra A, we denote by A* and A the first and the second duals of A respectively. Let T be a mapping from A* to itself. In this article, we will investigate some stability results concerning the equations

T(αfβg) = αT(f) + βT(g), T(af) = aT(f)

and

T(αfβg) + T(αf − βg) = 2α2T(f) + 2β2T(g)
where f, g ∈ A*, a ∈ A, and α, β∈ Q \ {0}.

Key words: Additive and quadratic mappings, Arens products, Banach algebra, multi-plier, stability

CLC Number: 

  • 39B82
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