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Generic differentiability of order-bounded convex oparators

Published online by Cambridge University Press:  17 February 2009

Jonathan M. Borwein
Dalhousie University, Canada
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We give sufficient conditions for order-bounded convex operators to be generically differentiable (Gâteaux or Fréchet). When the range space is a countably order-complete Banach lattice, these conditions are also necessary. In particular, every order-bounded convex operator from an Asplund space into such a lattice is generically Fréchet differentiable, if and only if the lattice has weakly-compact order intervals, if and only if the lattice has strongly-exposed order intervals. Applications are given which indicate how such results relate to optimization theory.

Research Article
Copyright © Australian Mathematical Society 1986


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