# Proof for banach Space 1

• May 8th 2010, 04:08 PM
neset44
Proof for banach Space 1
Prove that Xn converges to X then normed Xn converges to normed X

Anyone can help?
• May 8th 2010, 07:13 PM
Drexel28
Quote:

Originally Posted by neset44
Prove that Xn converges to X then normed Xn converges to normed X

Anyone can help?

This is horrible notation. I assume your saying that $\left\{x_n\right\}$ is a sequence in a Banach space $B$ and $x_n\to x$ and to prove that it follows that $\|x_n\|\to\|x\|$, right?

Hint:

Spoiler:

$|\|x_n\|-\|x\||\leqslant\|x_n-x\|$