Absolute Widths of Some Embeddings Original Research Article

The absolute widths of the natural identity operator Inpq, mapping lnp to lnq, for 1 ≤ q ≤ p ≤ ∞, are considered. The main result of this work is the following:THEOREM 1. If 1 ≤ q ≤ p ≤ ∞, 0 ≤ m ≤ n,dam(Inpq) = (n − m)1/q−1/q,wheredam(u) stands for the absolute width of the operator u.