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Posted: **Sun Jul 10, 2022 11:12 am**

: 6 17 Let X Coo With The Norm P 1 P Co For R 0 Consider The Linear Functional F On X Defined By Fr 2 J T 1 (33.2 KiB) Viewed 65 times

: 6 17 Let X Coo With The Norm P 1 P Co For R 0 Consider The Linear Functional F On X Defined By Fr 2 J T 2 (29.08 KiB) Viewed 65 times

6-17 Let X coo with the norm p, 1 ≤ p ≤ co. For r > 0, consider the linear functional f, on X defined by fr (2) = ²(j) T(1) js TEX. If p = 1, then f, is continuous and fr||1 = 1. If 1 < p ≤ oo, then f, is continuous if and only if r> 1-1/p= 1/g, and then 1/q (CA) ||fr|lp=
6-14 Let M = (kij) be an infinite matrix with scalar entries. If 1 < p < 0 and 1 ≤r<∞o, define --££~) Bp.r = r/q71/r where 1/p+1/9 = 1. If pr<oo, then M defines a continuous linear map from P to l' and its operator norm is at most pr.