Hi,(adsbygoogle = window.adsbygoogle || []).push({});

I'm stuck on a problem in functional analysis. Let x be a sequence on the Natural nummers such that for any square summable sequence y, the product sequence xy is absolutely summable. Then x is square summable.

Hint : Use the Closed graph theorem.

If I can prove the map Tx : y -> xy had a closed graph then It Follows from the Closed graph theorem that Tx is bounded and therefore that x is square summable, but I cant seem to show that the graph is Closed. Am I following the right path? Any hints?

Thanks

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Proof using the closed graph theorem

Loading...

**Physics Forums | Science Articles, Homework Help, Discussion**