Wydawnictwa / Banach Center Publications / Wszystkie tomy

Streszczenie

Let $X$ be a partially ordered real Banach space, $a,b \in X$ with $a \le b$. Let $\phi $ be a bounded linear functional on $X.$ We call $X$ a Ben-Israel-Charnes space (or a $B$-$C$ space) if the linear program defined by Maximize $ \phi(x)$ subject to $a \le x \le b$ has an optimal solution for any $\phi$, $a$ and $b.$ Such problems arise naturally in solving a class of problems known as Interval Linear Programs. $B$-$C$ spaces were introduced in the author's doctoral thesis and were subsequently studied in \cite{kcsjms1} and \cite{kcsjms2}. In this article, we review these results, study their implications to certain positive operators over partially ordered Banach spaces and obtain some new ones.