(ii)Since Cl(lin L) contains L, thus L◦up contains Cl(linL)◦up .
And if f is in L◦up, then f lies in Cl(linL)◦up for f is linear and coutinous. Thus Cl(linL)◦up contains L◦up. Q.E.D for the first conclusion.
Similarly for the second conclusion!
(iii) can also be proved By using the definition and the linearity and continuousity of Bounded linear function.