Moltó, A.; Orihuela, J.; Troyanski, S.; Zizler, V. Strictly convex renormings. (English) Zbl 1173.46001 J. Lond. Math. Soc., II. Ser. 75, No. 3, 647-658 (2007). The authors present the following characterization in linear topological terms of the normed spaces which are strictly convex renormable. Let \(X\) be a normed space and \(F\) a subspace of \(X^*\) which is 1-norming for \(X\). Then \(X\) admits an equivalent \(\sigma(X,F)\) lower semicontinuously strictly convex norm if, and only if \(X\) is sigma quasi-diagonal with respect to \((X,\sigma(X,F))\). Here a subset \(M\) of \(X^2\), where \(X\) is a linear topological space, is quasi-diagonal if it is symmetric, and if \(x=y\) whenever \((x,y)\in M\) and \(x,y\in \overline{\text{conv}}(DM)\), where \(D(x,y)=(x+y)/2\). A set \(M\) is sigma quasi-diagonal if it is a countable union of quasi-diagonal sets.The authors also consider the class of solid Banach lattices made up of bounded real functions on some set \(\Gamma\). They characterize the elements of this class which admit a pointwise strictly convex renorming. Reviewer: Anatolij M. Plichko (Krakow) Cited in 1 ReviewCited in 4 Documents MSC: 46B03 Isomorphic theory (including renorming) of Banach spaces 46B42 Banach lattices 46E05 Lattices of continuous, differentiable or analytic functions PDFBibTeX XMLCite \textit{A. Moltó} et al., J. Lond. Math. Soc., II. Ser. 75, No. 3, 647--658 (2007; Zbl 1173.46001) Full Text: DOI