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Tagged with lattices fa.functional-analysis
3 questions with no upvoted or accepted answers
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Questions related to a paper of Cowling-Haagerup and uniform lattices of $\mathrm{Sp}(1,n)$
I am reading the following paper of Cowling and Haagerup for my master’s thesis. I am new to this area so I am not very conversant. So I do apologize if the questions are silly.
Question 1. In the ...
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Is it possible that a convex cone and its closure both induce vector lattices?
Given a convex cone $P\subset X$ where $X$ is a $K$-vector space, $K=\mathbb{R}\text{ or }\mathbb{C}$ is a field.
Suppose that $P$ satisfies positive element stipulations.
(1) $X=P-P$.
(2) $P\cap-P=...
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Kirszbraun-like extension of periodic functions
Let $\Lambda \subset \Lambda' \subset \mathbb{R}^n$ be lattices. Let $f : \Lambda' \rightarrow \mathcal{H}$ be a $a$-Lipschitz function, where $\mathcal{H}$ is a finite-dimensional Hilbert Space. ...