prove that, in a Banach space if converges then converges
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Can you help me please?
prove that , in a Banach space if converges then converges.
Originally Posted by cizzzi prove that , in a Banach space if converges then converges. Show that the sum is Cauchy, i.e. consider , now consider . Hint: If then as k goes to infinity. (A fact that you can prove using the fact that ).
thank you I try to solve but I do not know very well functional analysis
Originally Posted by cizzzi thank you I try to solve but I do not know very well functional analysis Why don't you post what you have done so far (even if it is wrong)?
if X is complete and then sequence for is Cauchy because for k>m as therefore , exists in X. is it true?
Originally Posted by cizzzi if X is complete and then sequence for is Cauchy because for k>m as therefore , exists in X. is it true? The sum converges to zero as k and m tend to infinity (not zero).
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