Talk:Cotlar–Stein lemma

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[edit] Notability

Can someone explain in English why this article should be in wikipedia? --- Safemariner 06:15, 18 December 2006 (UTC)

OK, let's try this: the same reason as most articles. It explains the topic to those not already aware of it. Why do you single out this particular article? Your comments on my talk page suggest that you ought to start at some page like List of mathematics articles (E) (or you could start with "A") and ask that question about all of the thousands of articles you'll find listed there. Michael Hardy 06:22, 18 December 2006 (UTC)

It is my understanding that all articles have to be notable. I am just asking why this subject is notable. Also, not all Mathematics articles are inaccessible. This was one of the articles that I came across in a random search through math categories that was not a stub and I could not figure out what made this article notable. Since you have edited a lot of articles, do you know if there is a Wikipedia project page for Mathematics articles to discuss the issue of notability and accessibility of Mathematics articles? --- Safemariner 06:52, 18 December 2006 (UTC)

Certainly you can discuss this at Wikipedia talk:WikiProject Mathematics. Michael Hardy 01:28, 17 January 2007 (UTC)

... and as for your comments about accessibility, the question is accessible to whom? An article ideally should be made accessible to everyone who is ready to understand it. In a case like this, that would exclude most non-mathematicians. Michael Hardy 01:30, 17 January 2007 (UTC)

I found this article very useful. Thanks! —Preceding unsigned comment added by 190.16.40.238 (talk • contribs)

[edit] assumptions

seems to me one has to assume that the series ∑ T_i is convergent in the strong operator (or some other) topology. if so, that should be stated. the intro mentions an "almost orthogonality" condition, but no special condition was mentioned re the series ∑ T_i (other than that, one might guess, it converges in some sense). so what's the reason for this terminology? Mct mht 06:28, 17 January 2007 (UTC)

Thank you, very good points:

1. Rewrote so that the "almost orthogonality" condition becomes explicit.

2. Added the stanza about the convergence of ∑ T_i, which does not appear in Stein's book. The convergence does not need to be assumed; one can show that the convergence in the strong operator topology is a consequence of the almost orthogonality assumption. See http://www.math.tamu.edu/~comech/papers/CotlarStein/ (Comech 14:49, 28 January 2007 (UTC))

[edit] example

maybe a less trivial example is better? the one in the current version doesn't really shed light on the role of the "almost orthogonality" assumption. the given series obviously converges strongly to the identity operator. Mct mht 02:35, 24 June 2007 (UTC)