Extension of the operator of best polynomial approximation in

Let ( Ω , A , μ ) be a finite measure space. In this paper we extend the operator of the best generalized polynomial approximation from the space L p ( Ω ) to the space L p − 1 ( Ω ) , 1 < p < ∞ , as the unique operator preserving the property of continuity. The case p = 1 is also considered.