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 Isometric reflections in two dimensions and dual $\mathsf{L}^1$-structures Bull. Korean Math. Soc. 2012 Vol. 49, No. 6, 1275-1289 https://doi.org/10.4134/BKMS.2012.49.6.1275Printed November 30, 2012 Francisco J. Garc\'{i}a-Pacheco Texas A\&M University Abstract : In this manuscript we solve in the positive a question informally proposed by Enflo on the measure of the set of isometric reflection vectors in non-Hilbert $2$-dimensional real Banach spaces. We also reformulate equivalently the separable quotient problem in terms of isometric reflection vectors. Finally, we give a new and easy example of a real Banach space whose dual has a non-trivial $\mathsf{L}$-summand that does not come from an $M$-ideal in the predual. Keywords : isometric reflection vector, $\mathsf{L}^1$-summand vector MSC numbers : Primary 46B20, 46C05, 46B04 Downloads: Full-text PDF