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A note on the continuous self-maps of the ladder system space. (English) Zbl 1324.54055
Summary: We give a partial characterization of the continuous self-maps of the ladder system space \(K_{\mathcal S}\). Our results show that \(K_{\mathcal S}\) is highly nonrigid. We also discuss reasonable notions of “few operators” for spaces \(C(K)\) with scattered \(K\) and we show that \(C(K_{\mathcal S})\) does not have few operators for such notions.
MSC:
54G12 Scattered spaces
46E15 Banach spaces of continuous, differentiable or analytic functions
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