"Almost disjoint families and Banach spaces"Plebanek, GrzegorzTo every almost disjoint family $\mathcal A$ of subsets of the set of natural numbers one can associate a compact space $K_{\mathcal A}$ which is a scattered space with the third derivative empty. The plan is to discuss some properties of Banach spaces of the form $C(K_{\mathcal A})$. In particular, we will discuss the role of $C(K_{\mathcal A})$ spaces in our solution to a problem on twisted sums of $c_0$ and $C(K)$ spaces, obtained in collaboration with Antonio Aviles and Witold Marciszewski. We also present the following recent result of Alberto Salguero Alarcon and the speaker: There is a Banach space $C(K)$ and a complemented subspace $X$ of $C(K)$ such that $X$ is not isomorphic to a space of continuous functions. |
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