On a polygon equality problem

Elsner L, Han L, Koltracht I, Neumann M, Zippin M (1998)
Journal of Mathematical Analysis and Applications 223(1): 67-75.

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Zeitschriftenaufsatz | Veröffentlicht | Englisch
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Abstract / Bemerkung
Bernius and Blanchard of Bielefeld University in Germany have conjectured the following polygon inequality: for any two sets of vectors x(1),..., x(n) and y(1),..., y(n) in R-m, [GRAPHICS] in the 2-norm and that, moreover, equality holds in(*)if and only if there exists a permutation pi on {1, 2,..., n} such that y(i) = x(pi(i)), i = 1,..., n. That (*) is valid is a consequence of an inequality that holds in certain Banach spaces and which was recently proved by Lennard, Tongue, and Weston. We therefore characterize here the case of equality in (*), actually for vectors in the space X = L-1(Omega, mu), and subsequently use this characterization to complete the proof of the Bernius-Blanchard conjecture concerning the equality case in a Hilbert space. (C) 1998 Academic Press.
Erscheinungsjahr
Zeitschriftentitel
Journal of Mathematical Analysis and Applications
Band
223
Ausgabe
1
Seite(n)
67-75
ISSN
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Elsner L, Han L, Koltracht I, Neumann M, Zippin M. On a polygon equality problem. Journal of Mathematical Analysis and Applications. 1998;223(1):67-75.
Elsner, L., Han, L., Koltracht, I., Neumann, M., & Zippin, M. (1998). On a polygon equality problem. Journal of Mathematical Analysis and Applications, 223(1), 67-75. doi:10.1006/jmaa.1998.5955
Elsner, L., Han, L., Koltracht, I., Neumann, M., and Zippin, M. (1998). On a polygon equality problem. Journal of Mathematical Analysis and Applications 223, 67-75.
Elsner, L., et al., 1998. On a polygon equality problem. Journal of Mathematical Analysis and Applications, 223(1), p 67-75.
L. Elsner, et al., “On a polygon equality problem”, Journal of Mathematical Analysis and Applications, vol. 223, 1998, pp. 67-75.
Elsner, L., Han, L., Koltracht, I., Neumann, M., Zippin, M.: On a polygon equality problem. Journal of Mathematical Analysis and Applications. 223, 67-75 (1998).
Elsner, Ludwig, Han, Lixing, Koltracht, Israel, Neumann, Michael, and Zippin, Mori. “On a polygon equality problem”. Journal of Mathematical Analysis and Applications 223.1 (1998): 67-75.