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Analysis Functional
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answerhappygod
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Analysis Functional
Analysis Functional
Exercise 4. Let pe [1,00]. We define the space IP by IP = { x = (n)n: j=1 and sup|rj| if p = ∞}. j21 1. See if the sequences (Tn)n and (yn)n, given by Σ|xj|P<∞if1<p <∞ belong to 1. 2. See if the sequence (Tn)n given by belong to 12. 3. For x1, we put |||| In = = 1+ 2n, and yn = In = (-1)" n sup |xj| j21 Prove that (1, ||-||) is a normed vector space. 2n + 1
Exercise 4. Let pe [1,00]. We define the space IP by IP = { x = (n)n: j=1 and sup|rj| if p = ∞}. j21 1. See if the sequences (Tn)n and (yn)n, given by Σ|xj|P<∞if1<p <∞ belong to 1. 2. See if the sequence (Tn)n given by belong to 12. 3. For x1, we put |||| In = = 1+ 2n, and yn = In = (-1)" n sup |xj| j21 Prove that (1, ||-||) is a normed vector space. 2n + 1