| Abstrakt: |
In this paper we study maps Si:I⟶A, Ti:I⟶B, i=1,2on a non-empty set Iinto certain Banach function algebras Aand Bon compact Hausdorff spaces Xand Y, respectively, such that for some ε>0and all p,q∈Isatisfy d(Ranπ(T1(p)T2(q)),Ranπ(S1(p)S2(q)))⩽ε‖S1(p)S2(q)‖X, where Ranπ(.)stands for the peripheral range of functions. We first prove that, under some extra conditions, for i=1,2, Tiare almost composition or, almost weighted composition operators with respect to Siin a sense. We obtain some results on multiplicatively peripheral rang preserving maps as corollaries. Finally we show that the algebra of absolutely continuous functions on the unit interval and the algebra of Lipschitz functions satisfy the conditions of our theorems. So the results can be applied for these algebras. |
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