1. Consider the space of absolutely convergent sequences equipped with the following norm 1/2 00 I| (¤1, .., Tn, ..) |1,2= #;|+ (0.1) j=1 j=1 a). Prove that || - ||1.2 is a norm. b). Is this norm equivalent to the standard || r ||1= ET;[? 1/2 c). Is it equivalent to || | ||2= ( E;=1 T;|²

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