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Isometries for the Legendre-Fenchel transform. (English) Zbl 0607.49009

It is shown that the Legendre-Fenchel transform on the cone of proper lower semicontinuous convex functions on the Hilbert space X is an isometry with respect to some metrics which are equivalent to the epi- topology if X is finite-dimensional, and stronger than the Mosco-epi- topology in the infinite dimensional setting.
Reviewer: T.Zolezzi

MSC:

49J45 Methods involving semicontinuity and convergence; relaxation
49N15 Duality theory (optimization)
58E30 Variational principles in infinite-dimensional spaces
47H05 Monotone operators and generalizations
49J40 Variational inequalities
52A05 Convex sets without dimension restrictions (aspects of convex geometry)
90C31 Sensitivity, stability, parametric optimization
54A10 Several topologies on one set (change of topology, comparison of topologies, lattices of topologies)
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References:

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