Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
NCTM or The Math Forum.



Re: Infinite dimensional tensor analysis?
Posted:
Sep 10, 2012 1:26 PM


Shmuel (Seymour J.) Metz wrote: > As is well known, for a finite dimensional vector space V, there is a > canonical isomorphism between V and V**. One result of that is that > definitions of tensors using multilinear scalarvalued functions and > using quotient spaces of formal products are equivalent. In the > general[1][2] infinite dimensional case, that is not true. Which > definitions are normally used in Functional Analysis for infinite > dimensional tensors, and is there nomenclature specific to each > definition? > > [1] E.g., not assummg additional structure. > > [2] For topological vector spaces it is common to only include > continuous functions in the dual, and in a Hilbert space V > with that definition of dual, there is a canonical isomorphism > between V and V**. >
Speaking from the comfortable position of a knownothing, I found a Google search on
banach space tensor analysis
to produce a heap of possibilities. One that I found of likely use was the following:
http://www.math.jussieu.fr/~leila/grothendieckcircle/Diestel3.pdf
It's probably not as technically detailed as a practitioner would prefer, but its range of discussion & references should help.
Dale



