Non-nuclearity of a Sobolev embedding on an interval

• Non-nuclearity of a Sobolev embedding and the Hardy operator on the line is proved.
• An operator ideal norm generated by the approximation numbers is evaluated.
• The exact value of the nuclear norm for a certain operator is determined.

It is shown that the Sobolev embedding E:W0p1(I)→Lp(I)(I=(0,1),1≤p≤∞) is not nuclear. The same holds for the Hardy operator acting in Lp(I)Lp(I).