19.2.1.6 Properties of Normed Spaces

Condition: Show the equivalence of norms \ (\ | \ cdot \ | _ {1}, \ | \ cdot \ | _ {2} \) and \ (\ | \ cdot \ | _ {\ indy} \ quad \) in \ (\ quad \) of the red -free normalized space \ (x (x (x (x \), i.e. Find such positive constants \ (c_ {1} \) and \ (c_ {2} \) so that for any pair of norms \ (\ | \ cdot \ |^{\ prime} \) and \ | \ cdot \ |^{\ prime \ prime} \) a double was performed double Inequality \ (c_ {1} \ | x \ |^{\ prime} \ leq \ | x^\ |^{\ prime \ prime} \ leq c_ {2} \ | x \ |^{\ prime} \) for all \ (x \ in x \).