1. The problem statement, all variables and given/known data L : R^n → R is defined L(x1 , . . . , xn ) = sum (xj) from j=1 to n. The problem statement asks me to find an estimation for the operation norm of L, where on R the norm ll . llp, 1 ≤ p ≤ ∞, is used and on R the absolute value. 3. The attempt at a solution from, ll Lv lly ≤ M ll v llx I plan to find the smallest ''M'' since that's the operator norm. I assume that the linear operator is continuous. The problem statement mentions the Hölder inequality - as a hint. The truth is that I'm not sure what exactly I have to do in order to show what I plan to do. I have tried to do something but get stucked at the very begining... Any help will be very appreciated.