Re: Determinants in infinite dimensional spaces

yaroslavvb@xxxxxxxxx writes:

>Suppose we look at P = {p: p is a polynomial over R}
>Then let T = {t: t:P->P, t linear}
>
>Does there exist a determinant function on T?
>(unique multilinear alternating function d:T->R where d(1)=1)

What "multi" would you suggest for "multilinear" here?
On the endomorphisms of a vectorspace of finite dimension n,
det is n-linear...so, here...?

Relatedly, what "symmetric group" is acting on what,
in such a way that det can be said to be "alternating"?

These are not rhetorical, nor sarcastic, questions: you
may have answers (and they may be fine), but they aren't
immediately obvious to me at least.

>Are there any applications for such a function? Does it have any
>geometric interpretation like volume?

Lee Rudolph
.