Talk:Operator norm

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[edit] Some rewriting needed?

I wonder if this article needs some rewriting.

First, the article starts with a very technical "all operator norm definitions money can buy", which is certainly not encouraging.

Also, the first section does not tie in well with the remainder of the article in general.

Looking down below, one uses the words "bounded linear transformation" to introduce the notion of norm. Some care is needed here, as a bounded linear operator is not implying it to be a bounded linear function.

What could maybe make this article better is to split it into two articles. One main one about linear bounded operators where one focuses on linear operators and not as much on fine details about their norms, and a shorter article on operator norms, which could be more techical.

Other ideas? Oleg Alexandrov 03:30, 21 Feb 2005 (UTC)

I agree, really. The edit from last June which introduced the definition by symbols is not really in the right place. It should go after the more verbose definition. Also the first paragraph should be expanded with some gentle introduction to the general idea: the norm of an operator gives us a specific way to talk about its 'size', operator norms apply to matrices but also are particularly useful in picturing the case of spaces of infinite dimension, if the operator norm fails to be defined because the sup is unbounded that indicates the operator is not continuous.

Charles Matthews 09:15, 21 Feb 2005 (UTC)

Ah, I see that bounded operator redirects here. Well, that is a self-link that needs to be fixed. So, Oleg's idea maybe to split that into a separate article seems quite promising. Charles Matthews 09:18, 21 Feb 2005 (UTC)

I will get to it by this weeked. It would be not easy to separate linear operator from operator norm, as these go hand in hand. However, the way things are now is not so good, so two articles, even with a small amount of repetition among them, should be better. Oleg Alexandrov 19:05, 21 Feb 2005 (UTC)

[edit] Infimum and minimum

Just a minor thing: the second section says that $\{c : \|Av\| \leq c\|v\| \forall v \in V\}$ may have no minimum, but I dispute that. It's the intersection over all nonzero $v\in V$ of the closed set $[\|Av\| / \|v\|, \infty]$, and an abritrary intersection of closed sets is closed. David Bulger 00:59, 12 May 2006 (UTC)

You are right, I reworded the text appropriately. Oleg Alexandrov (talk) 02:54, 12 May 2006 (UTC)