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Cauchy sequence and translate

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Reference no: EM13956959

Show that (X, ||*||) is a Banach space if and only if {x in X: ||x||=1} is complete.

Know that in the first direction, we must show that {x in X: ||x||=1} is closed subset of X.

For the reverse direction, I know I have to take a cauchy sequence and translate it to the unit circle and then show that if it is convergent there, it is convergent outside of the unit circle.

Reference no: EM13956959

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