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Results tagged with positivity
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user 12248
8
votes
2
answers
1k
views
When is the norm of all positive operators on an ordered Banach space determined by their va...
I'm trying to investigate the interplay between the norm and cone of positive elements in ordered Banach spaces. In particular, I would like a nice characterization of when the norm of a positive oper …
6
votes
0
answers
118
views
$\ell^\infty / ces_0$ as an ordered Banach space
Let
$ces_0:=\{\xi\in\ell^\infty : \lim_{n\to \infty}\frac{1}{n}\sum_{k=1}^{n}\xi_k=0\}$ and $q:\ell^\infty \to \ell^\infty/ces_0$ be the usual quotient map. The space $ces_0$ is closed in $\ell^\inft …
1
vote
1
answer
112
views
Does every $\alpha$-normal ordered Banach space have minimal upper bounds?
Let $\alpha>0$ and $X$ be an $\alpha$-normal (meaning, for $x,y\in X$,
$0\leq x\leq y$ implies $\|x\|\leq\alpha\|y\|$) ordered Banach space
with closed generating cone $X_{+}$. If $X$ is reflexive, th …