Talk:Nuclear space

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[edit] Hilbert space

The article states:

There are no Banach spaces that are nuclear, except for the finite dimensional ones.

I'm naive, but isn't every Hilbert space going to be nuclear? Err, well, at least trace class? Or am I confused? And since Hilbert spaces are Banach spaces, the above statement sounds false to me. I'm confused ... linas 23:07, 24 October 2005 (UTC)

No, infinite dimensional Hilbert spaces are not nuclear. The identity operator of such a space is not trace class (or even compact). R.e.b. 01:09, 25 October 2005 (UTC)

Err, OK, thanks. I guess I was confused; I'll have to study a bit. linas 15:00, 25 October 2005 (UTC)

[edit] Banach spaces with seminorms?

The article states: If p is a seminorm on V, we write V_p for the Banach space given by completing V using the norm p. Now hold up, p is a seminorm, not a norm, so how on Earth is it going to make a Banach space? -lethe ^{talk +} 19:17, 7 March 2006 (UTC)

The process of completing a space automatically kills off the norm 0 vectors, so a seminorm on a space is (or more precisely induces) a norm on the competion. (Anyone confused by this is allowed to kill the norm 0 vectors before taking a completion.) R.e.b. 19:54, 2 April 2006 (UTC)

[edit] Link from "nuclear" ?

It would be useful to have a link from the disambiguation page of "nuclear" to this page (and to the page on nuclear operators). Sorry, but I myself don't know how to do that...