Analysis Functional
Posted: Mon Jul 11, 2022 12:51 pm
Analysis Functional
Exercise 3. For x = (x₁,...,n) ER", we put (Σ) j=1 ||||p 1. Let p = [1,00). Prove that = with q is given by += 1. 2. Prove that max |xj| 1≤j≤n if p = [1,00) if p = ∞o. n Vx,yR",xjyj|≤||||||||g₁ j=1 VIER", - ||1||1 ≤||1|||0 ≤ || ||p ≤ || ||1 ≤ n = ||2||p. 3. Prove that (R", ||-||p) is a normed vector space if 1 ≤p ≤ 0.
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