"Combinatorially dual spaces"Jachimek, SebastianLet $\mathcal{F}$ be a family of finite subsets of $\omega$ satysfing some good properties. A combinatorial space, denoted by $X_{\mathcal{F}}$, is a sequential Banach space being a completion of $c_{00}$ with respect to the norm $$ \lVert x \rVert_{\mathcal{F}} = \sup_{F \in \mathcal{F}} \sum_{k \in F} \lvert x(k) \rvert $$ During the talk we will present an example of a Banach space induced by $\mathcal{F}$ in a similar way and we give some of its properties. In particular we will see that it is \textit{close} to be a dual space to $X_{\mathcal{F}}$, in some sense. |
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