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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 …

The answer is that the reflexivity assumption cannot be dropped. The following simple example (due to Tony Wickstead) is a 1-normal non-reflexive space with closed and generating cone, where there ex …

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 …

After some digging, I found these two papers on the subject: Batty, Charles, and Derek Robinson. “Positive One-parameter Semigroups on Ordered Banach Spaces.” Acta Applicandae Mathematicae 2, no. 3 …

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 …