LOOK HERE: Analysis

  • Thread starter BobSun
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Homework Statement


Let X be a normed linear space. Prove that X is complete if and only if [tex]\sum^{\infty}_{n=1} x_{n}[/tex] converges in X for all sequences ([tex]x_{n}[/tex]) that satisfy [tex]\sum^{\infty}_{n=1} \left\|x_{n}\right\|[/tex]< [tex]\infty[/tex]
 

Answers and Replies

  • #2
morphism
Science Advisor
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What have you tried? This is actually a familiar fact from calculus. Do you remember how in R a series converged if it converged absolutely? And do you remember how that was proved? Same proof works here.
 

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