Two norms ||-||, and ||-||, on a vector space V are said to be equivalent if...
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Two norms ||-||, and ||-||, on a vector space V are said to be equivalent if there exist two positive constants c and C such that, (1) c||||≤||||₁ ≤C |||| for all x EV If the vector space V is R" show that, the norms ||·||||·||₁ and ||-||2 are equivalent. More precisely, show that, the following inequalities hold: b) ||||₁ √n ≤ x₂ ≤||||₁ for all x ER Two norms ||-||, and ||-||, on a vector space V are said to be equivalent if there exist two positive constants c and C such that, (1) c||||≤||||₁ ≤C |||| for all x EV If the vector space V is R" show that, the norms ||·||||·||₁ and ||-||2 are equivalent. More precisely, show that, the following inequalities hold: b) ||||₁ √n ≤ x₂ ≤||||₁ for all x ER
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