Burke, Maxim R.; Kubiś, Wiesław; Todorčević, Stevo Kadec norms on spaces of continuous functions. (English) Zbl 1164.46303 Serdica Math. J. 32, No. 2-3, 227-258 (2006). Summary: We study the existence of pointwise Kadec renormings for Banach spaces of the form \(C(K)\). We show in particular that such a renorming exists when \(K\) is any product of compact linearly ordered spaces, extending the result for a single factor due to Haydon, Jayne, Namioka and Rogers. We show that if \(C(K_1)\) has a pointwise Kadec renorming and \(K_2\) belongs to the class of spaces obtained by closing the class of compact metrizable spaces under inverse limits of transfinite continuous sequences of retractions, then \(C(K_1\times K_2)\) has a pointwise Kadec renorming. We also prove a version of the three-space property for such renormings. Cited in 6 Documents MSC: 46B03 Isomorphic theory (including renorming) of Banach spaces 46B26 Nonseparable Banach spaces 46E15 Banach spaces of continuous, differentiable or analytic functions 54C35 Function spaces in general topology Keywords:Banach space of continuous functions; compact space PDFBibTeX XMLCite \textit{M. R. Burke} et al., Serdica Math. J. 32, No. 2--3, 227--258 (2006; Zbl 1164.46303) Full Text: arXiv