Hi!

Two norms $\displaystyle ||\bullet ||$ and $\displaystyle |||\bullet |||$ on a vector space V are called equivalent if there exist 0 < a <= b such that

$\displaystyle a ||\bullet || \le |||\bullet ||| \le b ||\bullet || $

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$\displaystyle ||\bullet ||$ and $\displaystyle |||\bullet |||$ are equivalent

Show that

A sequence is a cauchy-sequence on $\displaystyle ||\bullet ||$ <=> A sequence is a cauchy-sequence on $\displaystyle |||\bullet |||$

I do not have any clue. Any help would be much appreciated.

best regards

Rapha