Talk:Banach–Mazur theorem
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Complex case
[edit]Is the same true for complex Banach spaces? The article mentions nothing about this case, I find this telling, so I guess its false. But it should still be mentioned in one way or the other.Scineram (talk) 12:00, 12 November 2008 (UTC)
Paths?
[edit]What is this misleading term "paths" doing in this article. It's like a tune deaf person singing, it's silly. Wlod (talk) 22:51, 4 January 2009 (UTC)
Paradoxical?
[edit]Formally, yes, the interesting theorem by Luis Rodríguez-Piazza is stronger than the original B-M Theorem. Nevertheless, in mathematical practice there is no reason to call it stronger, and certainly it is not a paradoxical theorem but, once such a question is posed, it is expected. I don't mean to down-grade this nice theorem but there is no reason to burden it with false compliments. As nice as L. R-P's theorem is, it is something of a curio, and it is not substantially stronger than the original theorem. (We all know for a long time that nice functions are exceptions, and that they form but a very thin subspace of the whole space of continuous functions). Wlod (talk) 23:00, 4 January 2009 (UTC)