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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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##### References:
 [1] A. V. Arkhangel’skii, Topological Function Spaces, Math. and its Appls. (Soviet Series), 78, Kluwer Academic Publishers (Dordrecht, 1992). [2] N. Dunford and J. T. Schwartz, Linear Operators, part I: General Theory, Pure and Applied Math. 7, Interscience Publishers (New York, 1958). [3] M. Fabian, P. Habala, P. Hájek, V. Montesinos and V. Zizler, Banach Space Theory: The Basis for Linear and Nonlinear Analysis, CMS Books in Math., Springer (New York, 2011). · Zbl 1229.46001 [4] Koszmider, P., A survey on Banach spaces $$C$$($$K$$) with few operators, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Math. RACSAM, 104, 309-326, (2010) · Zbl 1227.46021 [5] Koszmider, P.; Zieliński, P., Complementation and decompositions in some weakly Lindelöf Banach spaces, J. Math. Anal. Appl., 376, 329-341, (2011) · Zbl 1225.46012 [6] K. Kunen, Set Theory: An Introduction to Independence Proofs, Studies in Logic and the Found of Math. 102, North-Holland Publishing Company (Amsterdam, 1980). [7] Pol, R., A function space $$C$$($$X$$) which is weakly Lindelöf but not weakly compactly generated, Studia Math., 64, 279-285, (1979) · Zbl 0424.46011
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