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I am trying to understand in how far distributions form a coalgebra, and what can be derived from this viewpoint. The applicability of coalgebras to distribution theory seems to be one of the selling points of coalgebra and Hopf algebra theory, but I have yet to see a place where this is actually elaborated upon and applied to yield nontrivial results. More specifically, take a look at Chapt.

The Kernels Theorem".

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## DML-CZ - Czech Digital Mathematics Library: On a tensor product of weakly compact mappings

Home Questions Tags Users Unanswered. Distributions on product spaces Ask Question. Asked 8 years, 2 months ago. Active 8 years, 2 months ago.

## On a property of PLS-spaces inherited by their tensor products

Viewed 1k times. Andrey Rekalo Andrey Rekalo So there is no way to avoid nuclear theory if I want to see distributions as coalgebra?

The original proof of the Schwartz kernel theorem was obtained at the time when the TVS-based methodology had been 'in vogue'. Since then several more or less elementary presentations have appeared. This preview shows page 1 - 3 out of 11 pages. Subscribe to view the full document.

### Bulletin (New Series) of the American Mathematical Society

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University of Minnesota. MATH Uploaded By Stanley. Hilbert-Schmidt operators 2.