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# Talk:Banach space

## joke

a clever pun, to be sure, but i'm not sure it belongs in this article.

Q: What's yellow and normed, linear, and complete?

A: A Bananach Space.

And why it's yellow? -217.118.178.238 17:57, 26 Dec 2004 (UTC)
Bananach = banana + Banach. Bananas are typically yellow, Banach spaces are normed, linear, and complete. -Lethe | Talk

## norm in L(V,W)

dear Jitse Nielsen! please explain me, how we can divide norm of Ax (i.e., ||Ax||) to vector (not a number!) x? how we will get a number in this case? ||Ax||/x will not be a number, but ||Ax||/||x|| will. -217.118.178.238 22:14, 27 Dec 2004 (UTC)

I don't understand what you mean. You are right that one cannot divide a norm by a vector. Perhaps the notation
||A|| = sup { ||Ax|| : x in V with ||x|| ≤ 1 }
is not clear? The symbol : does not mean division, see set-builder notation. The definition for ||Ax|| can also be written as $\|A\| = \sup_{x \in B} \|Ax\|$, where B is the unit ball in V, so B is the set of all xV with ||x|| ≤ 1. -- Jitse Niesen 15:10, 28 Dec 2004 (UTC)
Last updated: 06-04-2005 17:51:18
03-10-2013 05:06:04