6-17 Let X = coo with the norm || ||p, 1 ≤p≤co. For r≥ 0, consider the linear functional fr on X defined by
fr (x) [infinity]Σ j=1 x(j)/j^r, x E X

If p = 1, then fr is continuous and ||fr||1= 1. If 1 < p ≤ [infinity]o, then fr is continuous if and only if r> 1-1/p=1/q, and then
IIfrIIp = (infinity Σ j=1 1/j^rq) ^1/q