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Topic: Infinite dimensional tensor analysis?
Replies: 3   Last Post: Sep 10, 2012 5:50 PM

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W. Dale Hall

Posts: 71
Registered: 2/11/05
Re: Infinite dimensional tensor analysis?
Posted: Sep 10, 2012 1:26 PM
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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 scalar-valued 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 know-nothing, 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



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