Abstract
We characterize the endomorphisms of the lattice of norms on reald-space where the lattice operations are determined by the usual ordering of real functions.
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References
G. Birkhoff, Lattice Theory, 3rd ed., Amer. Math. Soc. Providence Rh.I. 1967.
R. Fourneau, On the LatticeN(E) of J.J. Schäffer, Bull. Soc. Roy. Sci. Liege45 (1976), 312–316.
R. Fourneau, Isomorphisms of Lattices of Closed Convex Sets II, J. Math. Anal. Appl.61 (1977), 382–388.
R. Frank, Ein lokaler Fundamentalsatz für Projektionen, Manuskript 1990.
P.M. Gruber, The Endomorphisms of the Lattice of Convex Bodies, Abh. Math. Sem. Univ. Hamburg61 (1991), 121–130.
P.M. Gruber, The Space of Convex Bodies, in: Handbook of Convex Geometry, North-Holland Amsterdam, in preparation.
K. Leichtweiss, Konvexe Mengen, Springer Berlin 1980.
H. Lenz, Einige Anwendungen der projektiven Geometrie auf Fragen der Flächentheorie, Math. Nachr.18 (1958), 346–359.
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Gruber, P.M. The endomorphisms of the lattice of norms in finite dimensions. Abh.Math.Semin.Univ.Hambg. 62, 179–189 (1992). https://doi.org/10.1007/BF02941625
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DOI: https://doi.org/10.1007/BF02941625