APPROXIMATION OF ADJOINT OF A MULTIPLIER ON BANACH ALGEBRAS

doi:10.1016/S0252-9602(12)60058-7

Abstract

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

and

T(αf + βg) + 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

A. Ghaffari, S. Javadi, H. Khodaei. APPROXIMATION OF ADJOINT OF A MULTIPLIER ON BANACH ALGEBRAS[J].Acta mathematica scientia,Series B, 2012, 32(2): 783-792.

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