3.2.9. Given fixed indices 1

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3.2.9. Given fixed indices 1 <p<q<o∞, prove the following statements.
(a) (P C l.
(b) There exists a sequence r that belongs to (9 but not P.
(c) ||x||g < ||x||, for each r E lP. Hint: First consider sequences r that
satisfy ||a|| = 1.
Transcribed Image Text:3.2.9. Given fixed indices 1 <p<q<o∞, prove the following statements. (a) (P C l. (b) There exists a sequence r that belongs to (9 but not P. (c) ||x||g < ||x||, for each r E lP. Hint: First consider sequences r that satisfy ||a|| = 1.
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