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Abstract. We consider pairs of commuting contractions such that the joint left essential spectrum is dominating for the algebra H°°(D2). It is also assumed, in the first case, that one of them is C0, and the second one is absolutely continuous. In the second case, we assume that the pair is diagonally extendable. It will be shown that such pairs are reflexive.

We consider pairs of commuting contractions such that the joint left essential spectrum is dominating for the algebra H°°(D2). It is also assumed, in the first case, that one of them is C0, and the second one is absolutely continuous. In the second case, we assume that the pair is diagonally extendable. It will be shown that such pairs are reflexive. function f~(z) = f(z), z £ F .